# Find the prime factorization of 54 using exponents (2023)

### 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.

(Video) Prime Factorization Using Exponents

## 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:

(Video) Prime Factorization | Math with Mr. J

• 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 236 is not prime --> divide by 218 is not prime --> divide by 29 is not prime --> divide by 33 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:

(Video) Prime Factorization Using Exponents

 588/\2294/\2147/\349/\77 588 is not prime --> divide by 2294 is not prime --> divide by 2147 is not prime --> divide by 349 is not prime --> divide by 77 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

nPrime
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
nPrime
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
(Video) Prime Factorization (Intro and Factor Trees)
nPrime
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
nPrime
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

## 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
(Video) Write the Prime Power Factorization of 54

## 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 22 × 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.
1. Replace the numerator and denominator with their prime factorizations.
2. Cancel out any common factors in the numerator and denominator.
3. Multiply any leftover factors in the numerator together and any leftover factors in the denominator together.
Nov 23, 2021

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 is the smallest number among all common multiples of 54 and 27. The first few multiples of 54 and 27 are (54, 108, 162, 216, 270, . . . ) and (27, 54, 81, 108, 135, 162, 189, . . . ) respectively.
...
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 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? ›

Laws of Exponents
1. Bases – multiplying the like ones – add the exponents and keep the base same. ( Multiplication Law)
2. Bases – raise it with power to another – multiply the exponents and keep the base same.
3. Bases – dividing the like ones – 'Numerator Exponent – Denominator Exponent' and keep the base same. (
Feb 10, 2020

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 = 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.

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.

## Videos

1. Video 11: Expressing in Exponential Form
2. Math Antics - Prime Factorization
(mathantics)
3. Video 58: Finding LCM of Exponential Expressions
4. Prime Factorization 28 and 54
(MooMooMath and Science)
5. Prime Factorization and Exponents
6. How To Get Prime Factorizations And Use Exponents
(ChubbyGuy365)
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