Table of prime factors

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The tables contain the prime factorization of the natural numbers from 1 to 1000.

When n is a prime number, the prime factorization is just n itself, written in bold below.

The number 1 is called a unit. It has no prime factors and is neither prime nor composite.

See also: Table of divisors (prime and non-prime divisors for 1 to 1000)


Properties[edit]

Many properties of a natural number n can be seen or directly computed from the prime factorization of n.

  • The multiplicity of a prime factor p of n is the largest exponent m for which pm divides n. The tables show the multiplicity for each prime factor. If no exponent is written then the multiplicity is 1 (since p = p1). The multiplicity of a prime which does not divide n may be called 0 or may be considered undefined.
  • Ω(n), the big Omega function, is the number of prime factors of n counted with multiplicity (so it is the sum of all prime factor multiplicities).
  • A prime number has Ω(n) = 1. The first: 2, 3, 5, 7, 11 (sequence A000040 in OEIS). There are many special types of prime numbers.
  • A composite number has Ω(n) > 1. The first: 4, 6, 8, 9, 10 (sequence A002808 in OEIS). All numbers above 1 are either prime or composite. 1 is neither.
  • A semiprime has Ω(n) = 2 (so it is composite). The first: 4, 6, 9, 10, 14 (sequence A001358 in OEIS).
  • A k-almost prime (for a natural number k) has Ω(n) = k (so it is composite if k > 1).
  • An even number has the prime factor 2. The first: 2, 4, 6, 8, 10 (sequence A005843 in OEIS).
  • An odd number does not have the prime factor 2. The first: 1, 3, 5, 7, 9 (sequence A005408 in OEIS). All integers are either even or odd.
  • A square has even multiplicity for all prime factors (it is of the form a2 for some a). The first: 1, 4, 9, 16, 25 (sequence A000290 in OEIS).
  • A cube has all multiplicities divisible by 3 (it is of the form a3 for some a). The first: 1, 8, 27, 64, 125 (sequence A000578 in OEIS).
  • A perfect power has a common divisor m > 1 for all multiplicities (it is of the form am for some a > 1 and m > 1). The first: 4, 8, 9, 16, 25 (sequence A001597 in OEIS). 1 is sometimes included.
  • A powerful number (also called squareful) has multiplicity above 1 for all prime factors. The first: 1, 4, 8, 9, 16 (sequence A001694 in OEIS).
  • An Achilles number is powerful but not a perfect power. The first: 72, 108, 200, 288, 392 (sequence A052486 in OEIS).
  • A square-free integer has no prime factor with multiplicity above 1. The first: 1, 2, 3, 5, 6 (sequence A005117 in OEIS)). A number where some but not all prime factors have multiplicity above 1 is neither square-free nor squareful.
  • The Liouville function λ(n) is 1 if Ω(n) is even, and is -1 if Ω(n) is odd.
  • The Möbius function μ(n) is 0 if n is not square-free. Otherwise μ(n) is 1 if Ω(n) is even, and is −1 if Ω(n) is odd.
  • A sphenic number has Ω(n) = 3 and is square-free (so it is the product of 3 distinct primes). The first: 30, 42, 66, 70, 78 (sequence A007304 in OEIS).
  • a0(n) is the sum of primes dividing n, counted with multiplicity. It is an additive function.
  • A Ruth-Aaron pair is two consecutive numbers (x, x+1) with a0(x) = a0(x+1). The first (by x value): 5, 8, 15, 77, 125 (sequence A039752 in OEIS).
  • A primorial x# is the product of all primes from 2 to x. The first: 2, 6, 30, 210, 2310 (sequence A002110 in OEIS). 1# = 1 is sometimes included.
  • A factorial x! is the product of all numbers from 1 to x. The first: 1, 2, 6, 24, 120 (sequence A000142 in OEIS).
  • A k-smooth number (for a natural number k) has largest prime factor ≤ k (so it is also j-smooth for any j > k).
  • m is smoother than n if the largest prime factor of m is below the largest of n.
  • A regular number has no prime factor above 5 (so it is 5-smooth). The first: 1, 2, 3, 4, 5, 6, 8 (sequence A051037 in OEIS).
  • A k-powersmooth number has all pmk where p is a prime factor with multiplicity m.
  • A frugal number has more digits than the number of digits in its prime factorization (when written like below tables with multiplicities above 1 as exponents). The first in decimal: 125, 128, 243, 256, 343 (sequence A046759 in OEIS).
  • An equidigital number has the same number of digits as its prime factorization. The first in decimal: 1, 2, 3, 5, 7, 10 (sequence A046758 in OEIS).
  • An extravagant number has fewer digits than its prime factorization. The first in decimal: 4, 6, 8, 9, 12 (sequence A046760 in OEIS).
  • An economical number has been defined as a frugal number, but also as a number that is either frugal or equidigital.
  • gcd(m, n) (greatest common divisor of m and n) is the product of all prime factors which are both in m and n (with the smallest multiplicity for m and n).
  • m and n are coprime (also called relatively prime) if gcd(m, n) = 1 (meaning they have no common prime factor).
  • lcm(m, n) (least common multiple of m and n) is the product of all prime factors of m or n (with the largest multiplicity for m or n).
  • gcd(m, n) × lcm(m, n) = m × n. Finding the prime factors is often harder than to compute gcd and lcm with other algorithms which do not require known prime factorization.
  • m is a divisor of n (also called m divides n, or n is divisible by m) if all prime factors of m have at least the same multiplicity in n.

The divisors of n are all products of some or all prime factors of n (including the empty product 1 of no prime factors). The number of divisors can be computed by increasing all multiplicities by 1 and then multiplying them. Divisors and properties related to divisors are shown in table of divisors.

1 to 100[edit]

1 − 20
1 unit
2 2
3 3
4 22
5 5
6 2·3
7 7
8 23
9 32
10 2·5
11 11
12 22·3
13 13
14 2·7
15 3·5
16 24
17 17
18 2·32
19 19
20 22·5
21 − 40
21 3·7
22 2·11
23 23
24 23·3
25 52
26 2·13
27 33
28 22·7
29 29
30 2·3·5
31 31
32 25
33 3·11
34 2·17
35 5·7
36 22·32
37 37
38 2·19
39 3·13
40 23·5
41 − 60
41 41
42 2·3·7
43 43
44 22·11
45 32·5
46 2·23
47 47
48 24·3
49 72
50 2·52
51 3·17
52 22·13
53 53
54 2·33
55 5·11
56 23·7
57 3·19
58 2·29
59 59
60 22·3·5
61 − 80
61 61
62 2·31
63 32·7
64 26
65 5·13
66 2·3·11
67 67
68 22·17
69 3·23
70 2·5·7
71 71
72 23·32
73 73
74 2·37
75 3·52
76 22·19
77 7·11
78 2·3·13
79 79
80 24·5
81 − 100
81 34
82 2·41
83 83
84 22·3·7
85 5·17
86 2·43
87 3·29
88 23·11
89 89
90 2·32·5
91 7·13
92 22·23
93 3·31
94 2·47
95 5·19
96 25·3
97 97
98 2·72
99 32·11
100 22·52

If numbers are arranged in increasing columns of n numbers, then the prime factors of n will occur in the same row each time. The table columns have 20 = 22·5 numbers, so the prime factors 2 and 5 occur in fixed rows.

101 to 200[edit]

101 − 120
101 101
102 2·3·17
103 103
104 23·13
105 3·5·7
106 2·53
107 107
108 22·33
109 109
110 2·5·11
111 3·37
112 24·7
113 113
114 2·3·19
115 5·23
116 22·29
117 32·13
118 2·59
119 7·17
120 23·3·5
121 − 140
121 112
122 2·61
123 3·41
124 22·31
125 53
126 2·32·7
127 127
128 27
129 3·43
130 2·5·13
131 131
132 22·3·11
133 7·19
134 2·67
135 33·5
136 23·17
137 137
138 2·3·23
139 139
140 22·5·7
141 − 160
141 3·47
142 2·71
143 11·13
144 24·32
145 5·29
146 2·73
147 3·72
148 22·37
149 149
150 2·3·52
151 151
152 23·19
153 32·17
154 2·7·11
155 5·31
156 22·3·13
157 157
158 2·79
159 3·53
160 25·5
161 − 180
161 7·23
162 2·34
163 163
164 22·41
165 3·5·11
166 2·83
167 167
168 23·3·7
169 132
170 2·5·17
171 32·19
172 22·43
173 173
174 2·3·29
175 52·7
176 24·11
177 3·59
178 2·89
179 179
180 22·32·5
181 − 200
181 181
182 2·7·13
183 3·61
184 23·23
185 5·37
186 2·3·31
187 11·17
188 22·47
189 33·7
190 2·5·19
191 191
192 26·3
193 193
194 2·97
195 3·5·13
196 22·72
197 197
198 2·32·11
199 199
200 23·52

201 to 300[edit]

201 − 220
201 3·67
202 2·101
203 7·29
204 22·3·17
205 5·41
206 2·103
207 32·23
208 24·13
209 11·19
210 2·3·5·7
211 211
212 22·53
213 3·71
214 2·107
215 5·43
216 23·33
217 7·31
218 2·109
219 3·73
220 22·5·11
221 − 240
221 13·17
222 2·3·37
223 223
224 25·7
225 32·52
226 2·113
227 227
228 22·3·19
229 229
230 2·5·23
231 3·7·11
232 23·29
233 233
234 2·32·13
235 5·47
236 22·59
237 3·79
238 2·7·17
239 239
240 24·3·5
241 − 260
241 241
242 2·112
243 35
244 22·61
245 5·72
246 2·3·41
247 13·19
248 23·31
249 3·83
250 2·53
251 251
252 22·32·7
253 11·23
254 2·127
255 3·5·17
256 28
257 257
258 2·3·43
259 7·37
260 22·5·13
261 − 280
261 32·29
262 2·131
263 263
264 23·3·11
265 5·53
266 2·7·19
267 3·89
268 22·67
269 269
270 2·33·5
271 271
272 24·17
273 3·7·13
274 2·137
275 52·11
276 22·3·23
277 277
278 2·139
279 32·31
280 23·5·7
281 − 300
281 281
282 2·3·47
283 283
284 22·71
285 3·5·19
286 2·11·13
287 7·41
288 25·32
289 172
290 2·5·29
291 3·97
292 22·73
293 293
294 2·3·72
295 5·59
296 23·37
297 33·11
298 2·149
299 13·23
300 22·3·52

301 to 400[edit]

301 − 320
301 7·43
302 2·151
303 3·101
304 24·19
305 5·61
306 2·32·17
307 307
308 22·7·11
309 3·103
310 2·5·31
311 311
312 23·3·13
313 313
314 2·157
315 32·5·7
316 22·79
317 317
318 2·3·53
319 11·29
320 26·5
321 − 340
321 3·107
322 2·7·23
323 17·19
324 22·34
325 52·13
326 2·163
327 3·109
328 23·41
329 7·47
330 2·3·5·11
331 331
332 22·83
333 32·37
334 2·167
335 5·67
336 24·3·7
337 337
338 2·132
339 3·113
340 22·5·17
341 − 360
341 11·31
342 2·32·19
343 73
344 23·43
345 3·5·23
346 2·173
347 347
348 22·3·29
349 349
350 2·52·7
351 33·13
352 25·11
353 353
354 2·3·59
355 5·71
356 22·89
357 3·7·17
358 2·179
359 359
360 23·32·5
361 − 380
361 192
362 2·181
363 3·112
364 22·7·13
365 5·73
366 2·3·61
367 367
368 24·23
369 32·41
370 2·5·37
371 7·53
372 22·3·31
373 373
374 2·11·17
375 3·53
376 23·47
377 13·29
378 2·33·7
379 379
380 22·5·19
381 − 400
381 3·127
382 2·191
383 383
384 27·3
385 5·7·11
386 2·193
387 32·43
388 22·97
389 389
390 2·3·5·13
391 17·23
392 23·72
393 3·131
394 2·197
395 5·79
396 22·32·11
397 397
398 2·199
399 3·7·19
400 24·52

401 to 500[edit]

401 − 420
401 401
402 2·3·67
403 13·31
404 22·101
405 34·5
406 2·7·29
407 11·37
408 23·3·17
409 409
410 2·5·41
411 3·137
412 22·103
413 7·59
414 2·32·23
415 5·83
416 25·13
417 3·139
418 2·11·19
419 419
420 22·3·5·7
421 − 440
421 421
422 2·211
423 32·47
424 23·53
425 52·17
426 2·3·71
427 7·61
428 22·107
429 3·11·13
430 2·5·43
431 431
432 24·33
433 433
434 2·7·31
435 3·5·29
436 22·109
437 19·23
438 2·3·73
439 439
440 23·5·11
441 − 460
441 32·72
442 2·13·17
443 443
444 22·3·37
445 5·89
446 2·223
447 3·149
448 26·7
449 449
450 2·32·52
451 11·41
452 22·113
453 3·151
454 2·227
455 5·7·13
456 23·3·19
457 457
458 2·229
459 33·17
460 22·5·23
461 − 480
461 461
462 2·3·7·11
463 463
464 24·29
465 3·5·31
466 2·233
467 467
468 22·32·13
469 7·67
470 2·5·47
471 3·157
472 23·59
473 11·43
474 2·3·79
475 52·19
476 22·7·17
477 32·53
478 2·239
479 479
480 25·3·5
481 − 500
481 13·37
482 2·241
483 3·7·23
484 22·112
485 5·97
486 2·35
487 487
488 23·61
489 3·163
490 2·5·72
491 491
492 22·3·41
493 17·29
494 2·13·19
495 32·5·11
496 24·31
497 7·71
498 2·3·83
499 499
500 22·53

501 to 600[edit]

501 − 520
501 3·167
502 2·251
503 503
504 23·32·7
505 5·101
506 2·11·23
507 3·132
508 22·127
509 509
510 2·3·5·17
511 7·73
512 29
513 33·19
514 2·257
515 5·103
516 22·3·43
517 11·47
518 2·7·37
519 3·173
520 23·5·13
521 − 540
521 521
522 2·32·29
523 523
524 22·131
525 3·52·7
526 2·263
527 17·31
528 24·3·11
529 232
530 2·5·53
531 32·59
532 22·7·19
533 13·41
534 2·3·89
535 5·107
536 23·67
537 3·179
538 2·269
539 72·11
540 22·33·5
541 − 560
541 541
542 2·271
543 3·181
544 25·17
545 5·109
546 2·3·7·13
547 547
548 22·137
549 32·61
550 2·52·11
551 19·29
552 23·3·23
553 7·79
554 2·277
555 3·5·37
556 22·139
557 557
558 2·32·31
559 13·43
560 24·5·7
561 − 580
561 3·11·17
562 2·281
563 563
564 22·3·47
565 5·113
566 2·283
567 34·7
568 23·71
569 569
570 2·3·5·19
571 571
572 22·11·13
573 3·191
574 2·7·41
575 52·23
576 26·32
577 577
578 2·172
579 3·193
580 22·5·29
581 − 600
581 7·83
582 2·3·97
583 11·53
584 23·73
585 32·5·13
586 2·293
587 587
588 22·3·72
589 19·31
590 2·5·59
591 3·197
592 24·37
593 593
594 2·33·11
595 5·7·17
596 22·149
597 3·199
598 2·13·23
599 599
600 23·3·52

601 to 700[edit]

601 − 620
601 601
602 2·7·43
603 32·67
604 22·151
605 5·112
606 2·3·101
607 607
608 25·19
609 3·7·29
610 2·5·61
611 13·47
612 22·32·17
613 613
614 2·307
615 3·5·41
616 23·7·11
617 617
618 2·3·103
619 619
620 22·5·31
621 − 640
621 33·23
622 2·311
623 7·89
624 24·3·13
625 54
626 2·313
627 3·11·19
628 22·157
629 17·37
630 2·32·5·7
631 631
632 23·79
633 3·211
634 2·317
635 5·127
636 22·3·53
637 72·13
638 2·11·29
639 32·71
640 27·5
641 − 660
641 641
642 2·3·107
643 643
644 22·7·23
645 3·5·43
646 2·17·19
647 647
648 23·34
649 11·59
650 2·52·13
651 3·7·31
652 22·163
653 653
654 2·3·109
655 5·131
656 24·41
657 32·73
658 2·7·47
659 659
660 22·3·5·11
661 − 680
661 661
662 2·331
663 3·13·17
664 23·83
665 5·7·19
666 2·32·37
667 23·29
668 22·167
669 3·223
670 2·5·67
671 11·61
672 25·3·7
673 673
674 2·337
675 33·52
676 22·132
677 677
678 2·3·113
679 7·97
680 23·5·17
681 − 700
681 3·227
682 2·11·31
683 683
684 22·32·19
685 5·137
686 2·73
687 3·229
688 24·43
689 13·53
690 2·3·5·23
691 691
692 22·173
693 32·7·11
694 2·347
695 5·139
696 23·3·29
697 17·41
698 2·349
699 3·233
700 22·52·7

701 to 800[edit]

701 − 720
701 701
702 2·33·13
703 19·37
704 26·11
705 3·5·47
706 2·353
707 7·101
708 22·3·59
709 709
710 2·5·71
711 32·79
712 23·89
713 23·31
714 2·3·7·17
715 5·11·13
716 22·179
717 3·239
718 2·359
719 719
720 24·32·5
721 − 740
721 7·103
722 2·192
723 3·241
724 22·181
725 52·29
726 2·3·112
727 727
728 23·7·13
729 36
730 2·5·73
731 17·43
732 22·3·61
733 733
734 2·367
735 3·5·72
736 25·23
737 11·67
738 2·32·41
739 739
740 22·5·37
741 − 760
741 3·13·19
742 2·7·53
743 743
744 23·3·31
745 5·149
746 2·373
747 32·83
748 22·11·17
749 7·107
750 2·3·53
751 751
752 24·47
753 3·251
754 2·13·29
755 5·151
756 22·33·7
757 757
758 2·379
759 3·11·23
760 23·5·19
761 − 780
761 761
762 2·3·127
763 7·109
764 22·191
765 32·5·17
766 2·383
767 13·59
768 28·3
769 769
770 2·5·7·11
771 3·257
772 22·193
773 773
774 2·32·43
775 52·31
776 23·97
777 3·7·37
778 2·389
779 19·41
780 22·3·5·13
781 − 800
781 11·71
782 2·17·23
783 33·29
784 24·72
785 5·157
786 2·3·131
787 787
788 22·197
789 3·263
790 2·5·79
791 7·113
792 23·32·11
793 13·61
794 2·397
795 3·5·53
796 22·199
797 797
798 2·3·7·19
799 17·47
800 25·52

801 to 900[edit]

801 - 820
801 32·89
802 2·401
803 11·73
804 22·3·67
805 5·7·23
806 2·13·31
807 3·269
808 23·101
809 809
810 2·34·5
811 811
812 22·7·29
813 3·271
814 2·11·37
815 5·163
816 24·3·17
817 19·43
818 2·409
819 32·7·13
820 22·5·41
821 - 840
821 821
822 2·3·137
823 823
824 23·103
825 3·52·11
826 2·7·59
827 827
828 22·32·23
829 829
830 2·5·83
831 3·277
832 26·13
833 72·17
834 2·3·139
835 5·167
836 22·11·19
837 33·31
838 2·419
839 839
840 23·3·5·7
841 - 860
841 292
842 2·421
843 3·281
844 22·211
845 5·132
846 2·32·47
847 7·112
848 24·53
849 3·283
850 2·52·17
851 23·37
852 22·3·71
853 853
854 2·7·61
855 32·5·19
856 23·107
857 857
858 2·3·11·13
859 859
860 22·5·43
861 - 880
861 3·7·41
862 2·431
863 863
864 25·33
865 5·173
866 2·433
867 3·172
868 22·7·31
869 11·79
870 2·3·5·29
871 13·67
872 23·109
873 32·97
874 2·19·23
875 53·7
876 22·3·73
877 877
878 2·439
879 3·293
880 24·5·11
881 - 900
881 881
882 2·32·72
883 883
884 22·13·17
885 3·5·59
886 2·443
887 887
888 23·3·37
889 7·127
890 2·5·89
891 34·11
892 22·223
893 19·47
894 2·3·149
895 5·179
896 27·7
897 3·13·23
898 2·449
899 29·31
900 22·32·52

901 to 1000[edit]

901 - 920
901 17·53
902 2·11·41
903 3·7·43
904 23·113
905 5·181
906 2·3·151
907 907
908 22·227
909 32·101
910 2·5·7·13
911 911
912 24·3·19
913 11·83
914 2·457
915 3·5·61
916 22·229
917 7·131
918 2·33·17
919 919
920 23·5·23
921 - 940
921 3·307
922 2·461
923 13·71
924 22·3·7·11
925 52·37
926 2·463
927 32·103
928 25·29
929 929
930 2·3·5·31
931 72·19
932 22·233
933 3·311
934 2·467
935 5·11·17
936 23·32·13
937 937
938 2·7·67
939 3·313
940 22·5·47
941 - 960
941 941
942 2·3·157
943 23·41
944 24·59
945 33·5·7
946 2·11·43
947 947
948 22·3·79
949 13·73
950 2·52·19
951 3·317
952 23·7·17
953 953
954 2·32·53
955 5·191
956 22·239
957 3·11·29
958 2·479
959 7·137
960 26·3·5
961 - 980
961 312
962 2·13·37
963 32·107
964 22·241
965 5·193
966 2·3·7·23
967 967
968 23·112
969 3·17·19
970 2·5·97
971 971
972 22·35
973 7·139
974 2·487
975 3·52·13
976 24·61
977 977
978 2·3·163
979 11·89
980 22·5·72
981 - 1000
981 32·109
982 2·491
983 983
984 23·3·41
985 5·197
986 2·17·29
987 3·7·47
988 22·13·19
989 23·43
990 2·32·5·11
991 991
992 25·31
993 3·331
994 2·7·71
995 5·199
996 22·3·83
997 997
998 2·499
999 33·37
1000 23·53