### Prime Factorization Calculator

Here is the answer to questions like: Find the prime factorization of 54 using exponents or is 54 a prime or a composite number?

Use the Prime Factorization tool above to discover if any given number is prime or composite and in this case calculate the its prime factors. See also in this web page a Prime Factorization Chart with all primes from 1 to 1000.

## What is prime factorization?

### Definition of prime factorization

The prime factorization is the decomposition of a composite number into a product of prime factors that, if multiplied, recreate the original number. Factors by definition are the numbers that multiply to create another number. A prime number is an integer greater than one which is divided only by one and by itself. For example, the only divisors of 7 are 1 and 7, so 7 is a prime number, while the number 72 has divisors deived from 2^{3}•3^{2} like 2, 3, 4, 6, 8, 12, 24 ... and 72 itself, making 72 not a prime number. Note the the only "prime" factors of 72 are 2 and 3 which are prime numbers.

## Prime factorization example 1

Let's find the prime factorization of 72.

### Solution 1

Start with the smallest prime number that divides into 72, in this case 2. We can write 72 as:

72 = 2 x 36

Now find the smallest prime number that divides into 36. Again we can use 2, and write the 36 as 2 x 18, to give.

72 = 2 x 2 x 18

18 also divides by 2 (18 = 2 x 9), so we have:

72 = 2 x 2 x 2 x 9

9 divides by 3 (9 = 3 x 3), so we have:

72 = 2 x 2 x 2 x 3 x 3

2, 2, 2, 3 and 3 are all prime numbers, so we have our answer.

In short, we would write the solution as:

72 = 2 x 36

72 = 2 x 2 x 18

72 = 2 x 2 x 2 x 9

72 = 2 x 2 x 2 x 3 x 3

72 = 2^{3} x 3^{2} (prime factorization exponential form)

### Solution 2

Using a factor tree:

- Procedure:
- Find 2 factors of the number;
- Look at the 2 factors and determine if at least one of them is not prime;
- If it is not a prime factor it;
- Repeat this process until all factors are prime.

See how to factor the number 72:

72 /\ 236 /\ 218 /\ 29 /\ 33 | 72 is not prime --> divide by 2 36 is not prime --> divide by 2 18 is not prime --> divide by 2 9 is not prime --> divide by 3 3 and 3 are prime --> stop |

Taking the left-hand numbers and the right-most number of the last row (dividers) an multiplying then, we have

72 = 2 x 2 x 2 x 3 x 3

72 = 2^{3} x 3^{2} (prime factorization exponential form)

Note that these dividers are the prime factors. They are also called the leaves of the factor tree.

## Prime factorization example 2

See how to factor the number 588:

588 /\ 2294 /\ 2147 /\ 349 /\ 77 | 588 is not prime --> divide by 2 294 is not prime --> divide by 2 147 is not prime --> divide by 3 49 is not prime --> divide by 7 7 and 7 are prime --> stop |

Taking the left-hand numbers and the right-most number of the last row (dividers) an multiplying then, we have

588 = 2 x 2 x 3 x 7 x 7

588 = 2^{2} x 3 x 7^{2} (prime factorization exponential form)

## Prime Factorization Chart 1-1000

n | Prime Factorization |
---|---|

2 = | 2 |

3 = | 3 |

4 = | 2•2 |

5 = | 5 |

6 = | 2•3 |

7 = | 7 |

8 = | 2•2•2 |

9 = | 3•3 |

10 = | 2•5 |

11 = | 11 |

12 = | 2•2•3 |

13 = | 13 |

14 = | 2•7 |

15 = | 3•5 |

16 = | 2•2•2•2 |

17 = | 17 |

18 = | 2•3•3 |

19 = | 19 |

20 = | 2•2•5 |

21 = | 3•7 |

22 = | 2•11 |

23 = | 23 |

24 = | 2•2•2•3 |

25 = | 5•5 |

26 = | 2•13 |

27 = | 3•3•3 |

28 = | 2•2•7 |

29 = | 29 |

30 = | 2•3•5 |

31 = | 31 |

32 = | 2•2•2•2•2 |

33 = | 3•11 |

34 = | 2•17 |

35 = | 5•7 |

36 = | 2•2•3•3 |

37 = | 37 |

38 = | 2•19 |

39 = | 3•13 |

40 = | 2•2•2•5 |

41 = | 41 |

42 = | 2•3•7 |

43 = | 43 |

44 = | 2•2•11 |

45 = | 3•3•5 |

46 = | 2•23 |

47 = | 47 |

48 = | 2•2•2•2•3 |

49 = | 7•7 |

50 = | 2•5•5 |

51 = | 3•17 |

52 = | 2•2•13 |

53 = | 53 |

54 = | 2•3•3•3 |

55 = | 5•11 |

56 = | 2•2•2•7 |

57 = | 3•19 |

58 = | 2•29 |

59 = | 59 |

60 = | 2•2•3•5 |

61 = | 61 |

62 = | 2•31 |

63 = | 3•3•7 |

64 = | 2•2•2•2•2•2 |

65 = | 5•13 |

66 = | 2•3•11 |

67 = | 67 |

68 = | 2•2•17 |

69 = | 3•23 |

70 = | 2•5•7 |

71 = | 71 |

72 = | 2•2•2•3•3 |

73 = | 73 |

74 = | 2•37 |

75 = | 3•5•5 |

76 = | 2•2•19 |

77 = | 7•11 |

78 = | 2•3•13 |

79 = | 79 |

80 = | 2•2•2•2•5 |

81 = | 3•3•3•3 |

82 = | 2•41 |

83 = | 83 |

84 = | 2•2•3•7 |

85 = | 5•17 |

86 = | 2•43 |

87 = | 3•29 |

88 = | 2•2•2•11 |

89 = | 89 |

90 = | 2•3•3•5 |

91 = | 7•13 |

92 = | 2•2•23 |

93 = | 3•31 |

94 = | 2•47 |

95 = | 5•19 |

96 = | 2•2•2•2•2•3 |

97 = | 97 |

98 = | 2•7•7 |

99 = | 3•3•11 |

100 = | 2•2•5•5 |

101 = | 101 |

102 = | 2•3•17 |

103 = | 103 |

104 = | 2•2•2•13 |

105 = | 3•5•7 |

106 = | 2•53 |

107 = | 107 |

108 = | 2•2•3•3•3 |

109 = | 109 |

110 = | 2•5•11 |

111 = | 3•37 |

112 = | 2•2•2•2•7 |

113 = | 113 |

114 = | 2•3•19 |

115 = | 5•23 |

116 = | 2•2•29 |

117 = | 3•3•13 |

118 = | 2•59 |

119 = | 7•17 |

120 = | 2•2•2•3•5 |

121 = | 11•11 |

122 = | 2•61 |

123 = | 3•41 |

124 = | 2•2•31 |

125 = | 5•5•5 |

126 = | 2•3•3•7 |

127 = | 127 |

128 = | 2•2•2•2•2•2•2 |

129 = | 3•43 |

130 = | 2•5•13 |

131 = | 131 |

132 = | 2•2•3•11 |

133 = | 7•19 |

134 = | 2•67 |

135 = | 3•3•3•5 |

136 = | 2•2•2•17 |

137 = | 137 |

138 = | 2•3•23 |

139 = | 139 |

140 = | 2•2•5•7 |

141 = | 3•47 |

142 = | 2•71 |

143 = | 11•13 |

144 = | 2•2•2•2•3•3 |

145 = | 5•29 |

146 = | 2•73 |

147 = | 3•7•7 |

148 = | 2•2•37 |

149 = | 149 |

150 = | 2•3•5•5 |

151 = | 151 |

152 = | 2•2•2•19 |

153 = | 3•3•17 |

154 = | 2•7•11 |

155 = | 5•31 |

156 = | 2•2•3•13 |

157 = | 157 |

158 = | 2•79 |

159 = | 3•53 |

160 = | 2•2•2•2•2•5 |

161 = | 7•23 |

162 = | 2•3•3•3•3 |

163 = | 163 |

164 = | 2•2•41 |

165 = | 3•5•11 |

166 = | 2•83 |

167 = | 167 |

168 = | 2•2•2•3•7 |

169 = | 13•13 |

170 = | 2•5•17 |

171 = | 3•3•19 |

172 = | 2•2•43 |

173 = | 173 |

174 = | 2•3•29 |

175 = | 5•5•7 |

176 = | 2•2•2•2•11 |

177 = | 3•59 |

178 = | 2•89 |

179 = | 179 |

180 = | 2•2•3•3•5 |

181 = | 181 |

182 = | 2•7•13 |

183 = | 3•61 |

184 = | 2•2•2•23 |

185 = | 5•37 |

186 = | 2•3•31 |

187 = | 11•17 |

188 = | 2•2•47 |

189 = | 3•3•3•7 |

190 = | 2•5•19 |

191 = | 191 |

192 = | 2•2•2•2•2•2•3 |

193 = | 193 |

194 = | 2•97 |

195 = | 3•5•13 |

196 = | 2•2•7•7 |

197 = | 197 |

198 = | 2•3•3•11 |

199 = | 199 |

200 = | 2•2•2•5•5 |

201 = | 3•67 |

202 = | 2•101 |

203 = | 7•29 |

204 = | 2•2•3•17 |

205 = | 5•41 |

206 = | 2•103 |

207 = | 3•3•23 |

208 = | 2•2•2•2•13 |

209 = | 11•19 |

210 = | 2•3•5•7 |

211 = | 211 |

212 = | 2•2•53 |

213 = | 3•71 |

214 = | 2•107 |

215 = | 5•43 |

216 = | 2•2•2•3•3•3 |

217 = | 7•31 |

218 = | 2•109 |

219 = | 3•73 |

220 = | 2•2•5•11 |

221 = | 13•17 |

222 = | 2•3•37 |

223 = | 223 |

224 = | 2•2•2•2•2•7 |

225 = | 3•3•5•5 |

226 = | 2•113 |

227 = | 227 |

228 = | 2•2•3•19 |

229 = | 229 |

230 = | 2•5•23 |

231 = | 3•7•11 |

232 = | 2•2•2•29 |

233 = | 233 |

234 = | 2•3•3•13 |

235 = | 5•47 |

236 = | 2•2•59 |

237 = | 3•79 |

238 = | 2•7•17 |

239 = | 239 |

240 = | 2•2•2•2•3•5 |

241 = | 241 |

242 = | 2•11•11 |

243 = | 3•3•3•3•3 |

244 = | 2•2•61 |

245 = | 5•7•7 |

246 = | 2•3•41 |

247 = | 13•19 |

248 = | 2•2•2•31 |

249 = | 3•83 |

250 = | 2•5•5•5 |

n | Prime Factorization |
---|---|

251 = | 251 |

252 = | 2•2•3•3•7 |

253 = | 11•23 |

254 = | 2•127 |

255 = | 3•5•17 |

256 = | 2•2•2•2•2•2•2•2 |

257 = | 257 |

258 = | 2•3•43 |

259 = | 7•37 |

260 = | 2•2•5•13 |

261 = | 3•3•29 |

262 = | 2•131 |

263 = | 263 |

264 = | 2•2•2•3•11 |

265 = | 5•53 |

266 = | 2•7•19 |

267 = | 3•89 |

268 = | 2•2•67 |

269 = | 269 |

270 = | 2•3•3•3•5 |

271 = | 271 |

272 = | 2•2•2•2•17 |

273 = | 3•7•13 |

274 = | 2•137 |

275 = | 5•5•11 |

276 = | 2•2•3•23 |

277 = | 277 |

278 = | 2•139 |

279 = | 3•3•31 |

280 = | 2•2•2•5•7 |

281 = | 281 |

282 = | 2•3•47 |

283 = | 283 |

284 = | 2•2•71 |

285 = | 3•5•19 |

286 = | 2•11•13 |

287 = | 7•41 |

288 = | 2•2•2•2•2•3•3 |

289 = | 17•17 |

290 = | 2•5•29 |

291 = | 3•97 |

292 = | 2•2•73 |

293 = | 293 |

294 = | 2•3•7•7 |

295 = | 5•59 |

296 = | 2•2•2•37 |

297 = | 3•3•3•11 |

298 = | 2•149 |

299 = | 13•23 |

300 = | 2•2•3•5•5 |

301 = | 7•43 |

302 = | 2•151 |

303 = | 3•101 |

304 = | 2•2•2•2•19 |

305 = | 5•61 |

306 = | 2•3•3•17 |

307 = | 307 |

308 = | 2•2•7•11 |

309 = | 3•103 |

310 = | 2•5•31 |

311 = | 311 |

312 = | 2•2•2•3•13 |

313 = | 313 |

314 = | 2•157 |

315 = | 3•3•5•7 |

316 = | 2•2•79 |

317 = | 317 |

318 = | 2•3•53 |

319 = | 11•29 |

320 = | 2•2•2•2•2•2•5 |

321 = | 3•107 |

322 = | 2•7•23 |

323 = | 17•19 |

324 = | 2•2•3•3•3•3 |

325 = | 5•5•13 |

326 = | 2•163 |

327 = | 3•109 |

328 = | 2•2•2•41 |

329 = | 7•47 |

330 = | 2•3•5•11 |

331 = | 331 |

332 = | 2•2•83 |

333 = | 3•3•37 |

334 = | 2•167 |

335 = | 5•67 |

336 = | 2•2•2•2•3•7 |

337 = | 337 |

338 = | 2•13•13 |

339 = | 3•113 |

340 = | 2•2•5•17 |

341 = | 11•31 |

342 = | 2•3•3•19 |

343 = | 7•7•7 |

344 = | 2•2•2•43 |

345 = | 3•5•23 |

346 = | 2•173 |

347 = | 347 |

348 = | 2•2•3•29 |

349 = | 349 |

350 = | 2•5•5•7 |

351 = | 3•3•3•13 |

352 = | 2•2•2•2•2•11 |

353 = | 353 |

354 = | 2•3•59 |

355 = | 5•71 |

356 = | 2•2•89 |

357 = | 3•7•17 |

358 = | 2•179 |

359 = | 359 |

360 = | 2•2•2•3•3•5 |

361 = | 19•19 |

362 = | 2•181 |

363 = | 3•11•11 |

364 = | 2•2•7•13 |

365 = | 5•73 |

366 = | 2•3•61 |

367 = | 367 |

368 = | 2•2•2•2•23 |

369 = | 3•3•41 |

370 = | 2•5•37 |

371 = | 7•53 |

372 = | 2•2•3•31 |

373 = | 373 |

374 = | 2•11•17 |

375 = | 3•5•5•5 |

376 = | 2•2•2•47 |

377 = | 13•29 |

378 = | 2•3•3•3•7 |

379 = | 379 |

380 = | 2•2•5•19 |

381 = | 3•127 |

382 = | 2•191 |

383 = | 383 |

384 = | 2•2•2•2•2•2•2•3 |

385 = | 5•7•11 |

386 = | 2•193 |

387 = | 3•3•43 |

388 = | 2•2•97 |

389 = | 389 |

390 = | 2•3•5•13 |

391 = | 17•23 |

392 = | 2•2•2•7•7 |

393 = | 3•131 |

394 = | 2•197 |

395 = | 5•79 |

396 = | 2•2•3•3•11 |

397 = | 397 |

398 = | 2•199 |

399 = | 3•7•19 |

400 = | 2•2•2•2•5•5 |

401 = | 401 |

402 = | 2•3•67 |

403 = | 13•31 |

404 = | 2•2•101 |

405 = | 3•3•3•3•5 |

406 = | 2•7•29 |

407 = | 11•37 |

408 = | 2•2•2•3•17 |

409 = | 409 |

410 = | 2•5•41 |

411 = | 3•137 |

412 = | 2•2•103 |

413 = | 7•59 |

414 = | 2•3•3•23 |

415 = | 5•83 |

416 = | 2•2•2•2•2•13 |

417 = | 3•139 |

418 = | 2•11•19 |

419 = | 419 |

420 = | 2•2•3•5•7 |

421 = | 421 |

422 = | 2•211 |

423 = | 3•3•47 |

424 = | 2•2•2•53 |

425 = | 5•5•17 |

426 = | 2•3•71 |

427 = | 7•61 |

428 = | 2•2•107 |

429 = | 3•11•13 |

430 = | 2•5•43 |

431 = | 431 |

432 = | 2•2•2•2•3•3•3 |

433 = | 433 |

434 = | 2•7•31 |

435 = | 3•5•29 |

436 = | 2•2•109 |

437 = | 19•23 |

438 = | 2•3•73 |

439 = | 439 |

440 = | 2•2•2•5•11 |

441 = | 3•3•7•7 |

442 = | 2•13•17 |

443 = | 443 |

444 = | 2•2•3•37 |

445 = | 5•89 |

446 = | 2•223 |

447 = | 3•149 |

448 = | 2•2•2•2•2•2•7 |

449 = | 449 |

450 = | 2•3•3•5•5 |

451 = | 11•41 |

452 = | 2•2•113 |

453 = | 3•151 |

454 = | 2•227 |

455 = | 5•7•13 |

456 = | 2•2•2•3•19 |

457 = | 457 |

458 = | 2•229 |

459 = | 3•3•3•17 |

460 = | 2•2•5•23 |

461 = | 461 |

462 = | 2•3•7•11 |

463 = | 463 |

464 = | 2•2•2•2•29 |

465 = | 3•5•31 |

466 = | 2•233 |

467 = | 467 |

468 = | 2•2•3•3•13 |

469 = | 7•67 |

470 = | 2•5•47 |

471 = | 3•157 |

472 = | 2•2•2•59 |

473 = | 11•43 |

474 = | 2•3•79 |

475 = | 5•5•19 |

476 = | 2•2•7•17 |

477 = | 3•3•53 |

478 = | 2•239 |

479 = | 479 |

480 = | 2•2•2•2•2•3•5 |

481 = | 13•37 |

482 = | 2•241 |

483 = | 3•7•23 |

484 = | 2•2•11•11 |

485 = | 5•97 |

486 = | 2•3•3•3•3•3 |

487 = | 487 |

488 = | 2•2•2•61 |

489 = | 3•163 |

490 = | 2•5•7•7 |

491 = | 491 |

492 = | 2•2•3•41 |

493 = | 17•29 |

494 = | 2•13•19 |

495 = | 3•3•5•11 |

496 = | 2•2•2•2•31 |

497 = | 7•71 |

498 = | 2•3•83 |

499 = | 499 |

500 = | 2•2•5•5•5 |

n | Prime Factorization |
---|---|

501 = | 3•167 |

502 = | 2•251 |

503 = | 503 |

504 = | 2•2•2•3•3•7 |

505 = | 5•101 |

506 = | 2•11•23 |

507 = | 3•13•13 |

508 = | 2•2•127 |

509 = | 509 |

510 = | 2•3•5•17 |

511 = | 7•73 |

512 = | 2•2•2•2•2•2•2•2•2 |

513 = | 3•3•3•19 |

514 = | 2•257 |

515 = | 5•103 |

516 = | 2•2•3•43 |

517 = | 11•47 |

518 = | 2•7•37 |

519 = | 3•173 |

520 = | 2•2•2•5•13 |

521 = | 521 |

522 = | 2•3•3•29 |

523 = | 523 |

524 = | 2•2•131 |

525 = | 3•5•5•7 |

526 = | 2•263 |

527 = | 17•31 |

528 = | 2•2•2•2•3•11 |

529 = | 23•23 |

530 = | 2•5•53 |

531 = | 3•3•59 |

532 = | 2•2•7•19 |

533 = | 13•41 |

534 = | 2•3•89 |

535 = | 5•107 |

536 = | 2•2•2•67 |

537 = | 3•179 |

538 = | 2•269 |

539 = | 7•7•11 |

540 = | 2•2•3•3•3•5 |

541 = | 541 |

542 = | 2•271 |

543 = | 3•181 |

544 = | 2•2•2•2•2•17 |

545 = | 5•109 |

546 = | 2•3•7•13 |

547 = | 547 |

548 = | 2•2•137 |

549 = | 3•3•61 |

550 = | 2•5•5•11 |

551 = | 19•29 |

552 = | 2•2•2•3•23 |

553 = | 7•79 |

554 = | 2•277 |

555 = | 3•5•37 |

556 = | 2•2•139 |

557 = | 557 |

558 = | 2•3•3•31 |

559 = | 13•43 |

560 = | 2•2•2•2•5•7 |

561 = | 3•11•17 |

562 = | 2•281 |

563 = | 563 |

564 = | 2•2•3•47 |

565 = | 5•113 |

566 = | 2•283 |

567 = | 3•3•3•3•7 |

568 = | 2•2•2•71 |

569 = | 569 |

570 = | 2•3•5•19 |

571 = | 571 |

572 = | 2•2•11•13 |

573 = | 3•191 |

574 = | 2•7•41 |

575 = | 5•5•23 |

576 = | 2•2•2•2•2•2•3•3 |

577 = | 577 |

578 = | 2•17•17 |

579 = | 3•193 |

580 = | 2•2•5•29 |

581 = | 7•83 |

582 = | 2•3•97 |

583 = | 11•53 |

584 = | 2•2•2•73 |

585 = | 3•3•5•13 |

586 = | 2•293 |

587 = | 587 |

588 = | 2•2•3•7•7 |

589 = | 19•31 |

590 = | 2•5•59 |

591 = | 3•197 |

592 = | 2•2•2•2•37 |

593 = | 593 |

594 = | 2•3•3•3•11 |

595 = | 5•7•17 |

596 = | 2•2•149 |

597 = | 3•199 |

598 = | 2•13•23 |

599 = | 599 |

600 = | 2•2•2•3•5•5 |

601 = | 601 |

602 = | 2•7•43 |

603 = | 3•3•67 |

604 = | 2•2•151 |

605 = | 5•11•11 |

606 = | 2•3•101 |

607 = | 607 |

608 = | 2•2•2•2•2•19 |

609 = | 3•7•29 |

610 = | 2•5•61 |

611 = | 13•47 |

612 = | 2•2•3•3•17 |

613 = | 613 |

614 = | 2•307 |

615 = | 3•5•41 |

616 = | 2•2•2•7•11 |

617 = | 617 |

618 = | 2•3•103 |

619 = | 619 |

620 = | 2•2•5•31 |

621 = | 3•3•3•23 |

622 = | 2•311 |

623 = | 7•89 |

624 = | 2•2•2•2•3•13 |

625 = | 5•5•5•5 |

626 = | 2•313 |

627 = | 3•11•19 |

628 = | 2•2•157 |

629 = | 17•37 |

630 = | 2•3•3•5•7 |

631 = | 631 |

632 = | 2•2•2•79 |

633 = | 3•211 |

634 = | 2•317 |

635 = | 5•127 |

636 = | 2•2•3•53 |

637 = | 7•7•13 |

638 = | 2•11•29 |

639 = | 3•3•71 |

640 = | 2•2•2•2•2•2•2•5 |

641 = | 641 |

642 = | 2•3•107 |

643 = | 643 |

644 = | 2•2•7•23 |

645 = | 3•5•43 |

646 = | 2•17•19 |

647 = | 647 |

648 = | 2•2•2•3•3•3•3 |

649 = | 11•59 |

650 = | 2•5•5•13 |

651 = | 3•7•31 |

652 = | 2•2•163 |

653 = | 653 |

654 = | 2•3•109 |

655 = | 5•131 |

656 = | 2•2•2•2•41 |

657 = | 3•3•73 |

658 = | 2•7•47 |

659 = | 659 |

660 = | 2•2•3•5•11 |

661 = | 661 |

662 = | 2•331 |

663 = | 3•13•17 |

664 = | 2•2•2•83 |

665 = | 5•7•19 |

666 = | 2•3•3•37 |

667 = | 23•29 |

668 = | 2•2•167 |

669 = | 3•223 |

670 = | 2•5•67 |

671 = | 11•61 |

672 = | 2•2•2•2•2•3•7 |

673 = | 673 |

674 = | 2•337 |

675 = | 3•3•3•5•5 |

676 = | 2•2•13•13 |

677 = | 677 |

678 = | 2•3•113 |

679 = | 7•97 |

680 = | 2•2•2•5•17 |

681 = | 3•227 |

682 = | 2•11•31 |

683 = | 683 |

684 = | 2•2•3•3•19 |

685 = | 5•137 |

686 = | 2•7•7•7 |

687 = | 3•229 |

688 = | 2•2•2•2•43 |

689 = | 13•53 |

690 = | 2•3•5•23 |

691 = | 691 |

692 = | 2•2•173 |

693 = | 3•3•7•11 |

694 = | 2•347 |

695 = | 5•139 |

696 = | 2•2•2•3•29 |

697 = | 17•41 |

698 = | 2•349 |

699 = | 3•233 |

700 = | 2•2•5•5•7 |

701 = | 701 |

702 = | 2•3•3•3•13 |

703 = | 19•37 |

704 = | 2•2•2•2•2•2•11 |

705 = | 3•5•47 |

706 = | 2•353 |

707 = | 7•101 |

708 = | 2•2•3•59 |

709 = | 709 |

710 = | 2•5•71 |

711 = | 3•3•79 |

712 = | 2•2•2•89 |

713 = | 23•31 |

714 = | 2•3•7•17 |

715 = | 5•11•13 |

716 = | 2•2•179 |

717 = | 3•239 |

718 = | 2•359 |

719 = | 719 |

720 = | 2•2•2•2•3•3•5 |

721 = | 7•103 |

722 = | 2•19•19 |

723 = | 3•241 |

724 = | 2•2•181 |

725 = | 5•5•29 |

726 = | 2•3•11•11 |

727 = | 727 |

728 = | 2•2•2•7•13 |

729 = | 3•3•3•3•3•3 |

730 = | 2•5•73 |

731 = | 17•43 |

732 = | 2•2•3•61 |

733 = | 733 |

734 = | 2•367 |

735 = | 3•5•7•7 |

736 = | 2•2•2•2•2•23 |

737 = | 11•67 |

738 = | 2•3•3•41 |

739 = | 739 |

740 = | 2•2•5•37 |

741 = | 3•13•19 |

742 = | 2•7•53 |

743 = | 743 |

744 = | 2•2•2•3•31 |

745 = | 5•149 |

746 = | 2•373 |

747 = | 3•3•83 |

748 = | 2•2•11•17 |

749 = | 7•107 |

750 = | 2•3•5•5•5 |

n | Prime Factorization |
---|---|

751 = | 751 |

752 = | 2•2•2•2•47 |

753 = | 3•251 |

754 = | 2•13•29 |

755 = | 5•151 |

756 = | 2•2•3•3•3•7 |

757 = | 757 |

758 = | 2•379 |

759 = | 3•11•23 |

760 = | 2•2•2•5•19 |

761 = | 761 |

762 = | 2•3•127 |

763 = | 7•109 |

764 = | 2•2•191 |

765 = | 3•3•5•17 |

766 = | 2•383 |

767 = | 13•59 |

768 = | 2•2•2•2•2•2•2•2•3 |

769 = | 769 |

770 = | 2•5•7•11 |

771 = | 3•257 |

772 = | 2•2•193 |

773 = | 773 |

774 = | 2•3•3•43 |

775 = | 5•5•31 |

776 = | 2•2•2•97 |

777 = | 3•7•37 |

778 = | 2•389 |

779 = | 19•41 |

780 = | 2•2•3•5•13 |

781 = | 11•71 |

782 = | 2•17•23 |

783 = | 3•3•3•29 |

784 = | 2•2•2•2•7•7 |

785 = | 5•157 |

786 = | 2•3•131 |

787 = | 787 |

788 = | 2•2•197 |

789 = | 3•263 |

790 = | 2•5•79 |

791 = | 7•113 |

792 = | 2•2•2•3•3•11 |

793 = | 13•61 |

794 = | 2•397 |

795 = | 3•5•53 |

796 = | 2•2•199 |

797 = | 797 |

798 = | 2•3•7•19 |

799 = | 17•47 |

800 = | 2•2•2•2•2•5•5 |

801 = | 3•3•89 |

802 = | 2•401 |

803 = | 11•73 |

804 = | 2•2•3•67 |

805 = | 5•7•23 |

806 = | 2•13•31 |

807 = | 3•269 |

808 = | 2•2•2•101 |

809 = | 809 |

810 = | 2•3•3•3•3•5 |

811 = | 811 |

812 = | 2•2•7•29 |

813 = | 3•271 |

814 = | 2•11•37 |

815 = | 5•163 |

816 = | 2•2•2•2•3•17 |

817 = | 19•43 |

818 = | 2•409 |

819 = | 3•3•7•13 |

820 = | 2•2•5•41 |

821 = | 821 |

822 = | 2•3•137 |

823 = | 823 |

824 = | 2•2•2•103 |

825 = | 3•5•5•11 |

826 = | 2•7•59 |

827 = | 827 |

828 = | 2•2•3•3•23 |

829 = | 829 |

830 = | 2•5•83 |

831 = | 3•277 |

832 = | 2•2•2•2•2•2•13 |

833 = | 7•7•17 |

834 = | 2•3•139 |

835 = | 5•167 |

836 = | 2•2•11•19 |

837 = | 3•3•3•31 |

838 = | 2•419 |

839 = | 839 |

840 = | 2•2•2•3•5•7 |

841 = | 29•29 |

842 = | 2•421 |

843 = | 3•281 |

844 = | 2•2•211 |

845 = | 5•13•13 |

846 = | 2•3•3•47 |

847 = | 7•11•11 |

848 = | 2•2•2•2•53 |

849 = | 3•283 |

850 = | 2•5•5•17 |

851 = | 23•37 |

852 = | 2•2•3•71 |

853 = | 853 |

854 = | 2•7•61 |

855 = | 3•3•5•19 |

856 = | 2•2•2•107 |

857 = | 857 |

858 = | 2•3•11•13 |

859 = | 859 |

860 = | 2•2•5•43 |

861 = | 3•7•41 |

862 = | 2•431 |

863 = | 863 |

864 = | 2•2•2•2•2•3•3•3 |

865 = | 5•173 |

866 = | 2•433 |

867 = | 3•17•17 |

868 = | 2•2•7•31 |

869 = | 11•79 |

870 = | 2•3•5•29 |

871 = | 13•67 |

872 = | 2•2•2•109 |

873 = | 3•3•97 |

874 = | 2•19•23 |

875 = | 5•5•5•7 |

876 = | 2•2•3•73 |

877 = | 877 |

878 = | 2•439 |

879 = | 3•293 |

880 = | 2•2•2•2•5•11 |

881 = | 881 |

882 = | 2•3•3•7•7 |

883 = | 883 |

884 = | 2•2•13•17 |

885 = | 3•5•59 |

886 = | 2•443 |

887 = | 887 |

888 = | 2•2•2•3•37 |

889 = | 7•127 |

890 = | 2•5•89 |

891 = | 3•3•3•3•11 |

892 = | 2•2•223 |

893 = | 19•47 |

894 = | 2•3•149 |

895 = | 5•179 |

896 = | 2•2•2•2•2•2•2•7 |

897 = | 3•13•23 |

898 = | 2•449 |

899 = | 29•31 |

900 = | 2•2•3•3•5•5 |

901 = | 17•53 |

902 = | 2•11•41 |

903 = | 3•7•43 |

904 = | 2•2•2•113 |

905 = | 5•181 |

906 = | 2•3•151 |

907 = | 907 |

908 = | 2•2•227 |

909 = | 3•3•101 |

910 = | 2•5•7•13 |

911 = | 911 |

912 = | 2•2•2•2•3•19 |

913 = | 11•83 |

914 = | 2•457 |

915 = | 3•5•61 |

916 = | 2•2•229 |

917 = | 7•131 |

918 = | 2•3•3•3•17 |

919 = | 919 |

920 = | 2•2•2•5•23 |

921 = | 3•307 |

922 = | 2•461 |

923 = | 13•71 |

924 = | 2•2•3•7•11 |

925 = | 5•5•37 |

926 = | 2•463 |

927 = | 3•3•103 |

928 = | 2•2•2•2•2•29 |

929 = | 929 |

930 = | 2•3•5•31 |

931 = | 7•7•19 |

932 = | 2•2•233 |

933 = | 3•311 |

934 = | 2•467 |

935 = | 5•11•17 |

936 = | 2•2•2•3•3•13 |

937 = | 937 |

938 = | 2•7•67 |

939 = | 3•313 |

940 = | 2•2•5•47 |

941 = | 941 |

942 = | 2•3•157 |

943 = | 23•41 |

944 = | 2•2•2•2•59 |

945 = | 3•3•3•5•7 |

946 = | 2•11•43 |

947 = | 947 |

948 = | 2•2•3•79 |

949 = | 13•73 |

950 = | 2•5•5•19 |

951 = | 3•317 |

952 = | 2•2•2•7•17 |

953 = | 953 |

954 = | 2•3•3•53 |

955 = | 5•191 |

956 = | 2•2•239 |

957 = | 3•11•29 |

958 = | 2•479 |

959 = | 7•137 |

960 = | 2•2•2•2•2•2•3•5 |

961 = | 31•31 |

962 = | 2•13•37 |

963 = | 3•3•107 |

964 = | 2•2•241 |

965 = | 5•193 |

966 = | 2•3•7•23 |

967 = | 967 |

968 = | 2•2•2•11•11 |

969 = | 3•17•19 |

970 = | 2•5•97 |

971 = | 971 |

972 = | 2•2•3•3•3•3•3 |

973 = | 7•139 |

974 = | 2•487 |

975 = | 3•5•5•13 |

976 = | 2•2•2•2•61 |

977 = | 977 |

978 = | 2•3•163 |

979 = | 11•89 |

980 = | 2•2•5•7•7 |

981 = | 3•3•109 |

982 = | 2•491 |

983 = | 983 |

984 = | 2•2•2•3•41 |

985 = | 5•197 |

986 = | 2•17•29 |

987 = | 3•7•47 |

988 = | 2•2•13•19 |

989 = | 23•43 |

990 = | 2•3•3•5•11 |

991 = | 991 |

992 = | 2•2•2•2•2•31 |

993 = | 3•331 |

994 = | 2•7•71 |

995 = | 5•199 |

996 = | 2•2•3•83 |

997 = | 997 |

998 = | 2•499 |

999 = | 3•3•3•37 |

1000 = | 2•2•2•5•5•5 |

### Prime Factorization Calculator

Please link to this page! Just right click on the above image, choose copy link address, then past it in your HTML.

## Sample Number Factorizations.

- Prime factorization of 615
- Prime factorization of 15
- Prime factorization of 832040

- Prime factorization of 123
- Prime factorization of 916
- Prime factorization of 590

- Prime factorization of 37860
- Prime factorization of 2584
- Prime factorization of 75025

## FAQs

### What is the prime factorization of 54? ›

Prime factorisation of 54 is **2 × 3 × 3 × 3**. Therefore, the highest prime factor of 54 is 3.

**What is 54 using exponents? ›**

That is, 54 = 2 × 27 = **2 × 33**. Thus, we have that the prime factorization of 54, using exponents, is 2 × 33.

**What is the prime factorization using exponents of 560? ›**

Answer and Explanation: The prime factorization of 560 using exponents is **24∗5∗7** 2 4 ∗ 5 ∗ 7 .

**What is the sum of exponents of prime factors in the prime factorization of 54? ›**

Sum of Factors of 54: **120**

What Are the Factors of 54?

**What is 2 with an exponent of 54? ›**

The first step is to understand what it means when a number has an exponent. The “power” of a number indicates how many times the base would be multiplied by itself to reach the correct value. Therefore, 2 to the power of 54 is **18014398509481984**.

**What multiply equals 54? ›**

54 is a composite number. 54 = 1 x 54, 2 x 27, 3 x 18, or 6 x 9.

**What is the prime factorization of 56 using exponents? ›**

The prime factorization of 56 is 2 * 2 * 2 * 7. This can also be written with exponents as **2^3 * 7**.

**What is an example of a prime factorization in math? ›**

Prime factorization is a process of writing all numbers as a product of primes. So, for example, **say if we have something like the number 20.** **We can break that down into two factors.** **We can say, “well, that's 4 times 5**.” And notice, 5 is a prime number.

**What is the prime factor of 50 using exponents? ›**

Exponential Form of 50

As we know, the prime factorization of the 50 is **2 5 5**. Accordingly, the prime factorization of 50 in exponential form is written as 2¹ x 5².

**What is the prime factorization of 45 using exponents? ›**

The prime factorization of 45 in exponential form is **3^2 x 5**.

### What is the prime factorization of 25 using exponents? ›

Answer and Explanation: The prime factorization of 25 is **5 × 5**. The three methods we can use to find the prime factorization of a number x depend on x itself.

**What is the prime factorization of 35 using exponents? ›**

The prime factorization of 35 is **5 × 7**.

**What is the prime factorization of 52 exponents? ›**

The prime factorization of 52 is **2 × 2 × 13** or 2^{2} × 13.

**Is 54 a perfect square? ›**

54 is a **non-square number**.

**How do you simplify using prime factorization? ›**

**To use prime factorization to reduce a fraction, we follow these steps.**

- Replace the numerator and denominator with their prime factorizations.
- Cancel out any common factors in the numerator and denominator.
- Multiply any leftover factors in the numerator together and any leftover factors in the denominator together.

**What is the percentage of 2 54? ›**

Solution: 2/54 as a percent is **3.704%**

**Is ² an exponent? ›**

For any variable x, x squared or is a mathematical notation that refers to a number being multiplied by itself. It represents the expression “ x × x ” or “x times x”. x squared symbol is . Here, is known as the base, and **2 is called the exponent**.

**What is the tree factor of 54? ›**

All these factor trees will result to 54=**2×33**.

**Is 54 a least common multiple? ›**

...

LCM of 54 and 27.

1. | LCM of 54 and 27 |
---|---|

2. | List of Methods |

3. | Solved Examples |

4. | FAQs |

**What number will multiply 54 to make it a perfect square? ›**

We need to find factors of 54 that are perfect squares . With a little bit of guess and check if you did not know this already, 54 is divisible by 9 , and **9** is a perfect square ( 3⋅3 ).

### What is an exponent simple answer? ›

Exponent is defined as **the method of expressing large numbers in terms of powers**. That means, exponent refers to how many times a number multiplied by itself. For example, 6 is multiplied by itself 4 times, i.e. 6 × 6 × 6 × 6. This can be written as 6^{4}. Here, 4 is the exponent and 6 is the base.

**What are exponents in math grade 7? ›**

An exponent **tells you how many times its base is used as a factor**. Exponents are used to write repeated multiplication.

**How do you solve exponents and powers easily? ›**

**Laws of Exponents**

- Bases – multiplying the like ones – add the exponents and keep the base same. ( Multiplication Law)
- Bases – raise it with power to another – multiply the exponents and keep the base same.
- Bases – dividing the like ones – 'Numerator Exponent – Denominator Exponent' and keep the base same. (

**What is the prime factorization of 48 using exponents? ›**

So, 48=2∗2∗2∗2∗3 48 = 2 ∗ 2 ∗ 2 ∗ 2 ∗ 3 . And to write this prime factorization in exponential form, show the repeated multiplication of 2∗2∗2∗2 2 ∗ 2 ∗ 2 ∗ 2 as 24 . Finally, the prime factorization of 48 in exponential form is **24∗3 2 4 ∗ 3** .

**What is the prime factorization of 42 using exponents? ›**

The prime factorization of 42 is **2 × 3 × 7**.

**What is the prime factorization of 51 using exponents? ›**

Hence, the prime factorization of 51 is 51 = **3 × 17**.

**What is prime factorization grade 6? ›**

Prime Factorization **One way of describing numbers is by breaking them down into a product of their prime factors**. This is called prime factorization. Every positive number can be prime factored. By definition the prime factorization of a prime number is the number itself, and the prime factorization of 1 is 1.

**What is the prime factorization of 24 using exponents? ›**

Answer and Explanation: The prime factorization of the number 24 is 2 × 2 × 2 × 3. You can also write this with exponents as **23 × 3**.

**What is the prime factorization of 15 using exponents? ›**

Answer and Explanation: The prime factorization of 15 is **3 × 5**. There are no exponents, because there are no repeated primes. Notice that the number 3 and the number 5 are both prime numbers, and that 3 × 5 = 15.

**What is the prime factorization of 40 using exponents? ›**

The number 40 can be written in prime factorization as 2 x 2 x 2 x 5. All of the factors are prime numbers. Using exponential form, 40 = **2 ^{3}5^{1}**, indicating that there are three 2's and one 5 multilplied together to get the result of 40.

### What is the prime factorization of 27 using exponents? ›

Answer and Explanation: The prime factorization of 27 is **3 * 3 * 3**, or 3^3.

**What is the prime factorization of 32 using exponents? ›**

The prime factorization of 32 can be written as **2^5**, or 2 * 2 * 2 * 2 * 2.

**What is the prime factorization of 75 using exponents? ›**

Answer and Explanation: The prime factorization with exponents is **3∗52** 3 ∗ 5 2 .

**What is the prime factorization of 60 using exponents? ›**

Answer and Explanation: The prime factorization of 60 in exponential form is **2^2 x 3 x 5**.

**What is the prime factorization of 36 using exponents? ›**

In the prime factorization of 36 = **2² × 3²**, both of the factors 2 and 3 have an exponent of two because each factor appears twice.

**What is the prime factorization of 72 using exponents? ›**

Answer and Explanation: The prime factorization of 72 in exponential form is **23 × 32**. In general, we use factor trees to find the prime factorization of a number in exponential form by following these steps: Write the number down.

**What is the prime factorization of 39 using exponents? ›**

Thus, the prime factorisation of 39 can be expressed as **3 × 13**.

**What is the prime factorization of 70 using exponents? ›**

So, the prime factors of 70 are written as 2 x 5 x 7, where 2, 5 and 7 are the prime numbers. It is possible to find the exact number of factors of a number 70 with the help of prime factorisation. The prime factor of the 70 is 2 x 5 x 7. The exponents in the prime factorisation are **1, 1 and 1**.

**What is the prime factorization of 18 using exponents? ›**

Answer and Explanation: The prime factorization of 18 with exponents is **2 × 32**. There are a few different ways of finding the prime factorization of a number.

**What is the prime or composite of 54? ›**

Yes, since 54 has more than two factors i.e. 1, 2, 3, 6, 9, 18, 27, 54. In other words, 54 is a **composite number** because 54 has more than 2 factors.

### What is the prime factorization of 45 and 54? ›

How to Find the GCF of 54 and 45 by Prime Factorization? To find the GCF of 54 and 45, we will find the prime factorization of the given numbers, i.e. 54 = 2 × 3 × 3 × 3; 45 = 3 × 3 × 5.

**What is the prime factorization of 54 and 36? ›**

Prime factors of 54 are **2×3×3×3** . Prime factors of 36 are 2×2×3×3 . We have to multiply all the common factors to get the HCF. Therefore, the greatest common factors of 54 and 36 are 2×3×3=18 .

**What is the prime factorization of 54 and 27? ›**

There are 4 common factors of 54 and 27, that are **3, 1, 27, and 9**. Therefore, the greatest common factor of 54 and 27 is 27.

**What is 54 a multiple of? ›**

54 is a factor and a multiple of 5 and 4 also.

**What composite comes after 54? ›**

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

**What is the least common multiple of 54? ›**

The LCM of 54 and 27 is **54**. To find the LCM (least common multiple) of 54 and 27, we need to find the multiples of 54 and 27 (multiples of 54 = 54, 108, 162, 216; multiples of 27 = 27, 54, 81, 108) and choose the smallest multiple that is exactly divisible by 54 and 27, i.e., 54.

**What is the prime factorization of 54 and 81? ›**

The GCF of 54 and 81 is 27. To calculate the greatest common factor of 54 and 81, we need to factor each number (factors of 54 = **1, 2, 3, 6, 9, 18, 27, 54**; factors of 81 = 1, 3, 9, 27, 81) and choose the greatest factor that exactly divides both 54 and 81, i.e., 27.

**What is the prime factorization of 54 and 72? ›**

Prime factorization of 54 and 72 is **(2 × 3 × 3 × 3) and (2 × 2 × 2 × 3 × 3)** respectively. As visible, 54 and 72 have common prime factors. Hence, the GCF of 54 and 72 is 2 × 3 × 3 = 18.

**What is the prime factorization of 48 and 54? ›**

The common prime factors of 48 and 54 are **2 and 3**.

**What is the prime factorization of 18 and 54? ›**

HCF of 18 and 54 by Prime Factorisation Method

The common prime factors of 18 and 54 are **2, 3 and 3**.

### What is the prime factorization of 54 and 90? ›

Prime factorization of 54 and 90 is **(2 × 3 × 3 × 3) and (2 × 3 × 3 × 5)** respectively. As visible, 54 and 90 have common prime factors. Hence, the GCF of 54 and 90 is 2 × 3 × 3 = 18.

**How do you find the greatest common factor of 54? ›**

When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 3, 6, 9, 18, 27, 54. Since 54 is the largest of these common factors, the GCF of 54 and 54 would be 54.

**What is the prime factorization 12 54? ›**

GCF of 12 and 54 by Prime Factorization

Prime factorization of 12 and 54 is **(2 × 2 × 3)** and (2 × 3 × 3 × 3) respectively. As visible, 12 and 54 have common prime factors. Hence, the GCF of 12 and 54 is 2 × 3 = 6.

**What are the prime factorization of 42 and 54? ›**

Prime factorization of 42 and 54 is **(2 × 3 × 7) and (2 × 3 × 3 × 3)** respectively. As visible, 42 and 54 have common prime factors. Hence, the GCF of 42 and 54 is 2 × 3 = 6.