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 23•32 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 = 23 x 32 (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 = 23 x 32 (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 = 22 x 3 x 72 (prime factorization exponential form)
Prime Factorization Chart 1-1000
n Prime
Factorization2 = 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
Factorization251 = 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
Factorization501 = 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
Factorization751 = 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
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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?
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.
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 22 × 13.
Is 54 a perfect square? ›54 is a non-square number.
How do you simplify using prime factorization? ›- 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.
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 |
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 64. 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? ›- 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. (
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 = 2351, 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.
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.