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.

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 p divides n. The tables show the multiplicity for each prime factor. If no exponent is written then the multiplicity is 1 (since p = p). The multiplicity of a prime which does not divide n may be called 0 or may be considered undefined.
• Ω(n), the prime 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, 13, 17, 19, 23, 29, 31, 37 (sequence A000040 in the OEIS). There are many special types of prime numbers.
• A composite number has Ω(n) > 1. The first: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21 (sequence A002808 in the 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, 15, 21, 22, 25, 26, 33, 34 (sequence A001358 in the 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, 12, 14, 16, 18, 20, 22, 24 (sequence A005843 in the OEIS).
• An odd number does not have the prime factor 2. The first: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 (sequence A005408 in the OEIS). All integers are either even or odd.
• A square has even multiplicity for all prime factors (it is of the form a for some a). The first: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 (sequence A000290 in the OEIS).
• A cube has all multiplicities divisible by 3 (it is of the form a for some a). The first: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728 (sequence A000578 in the OEIS).
• A perfect power has a common divisor m > 1 for all multiplicities (it is of the form a for some a > 1 and m > 1). The first: 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81, 100 (sequence A001597 in the 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, 25, 27, 32, 36, 49, 64, 72 (sequence A001694 in the OEIS).
• A prime power has only one prime factor. The first: 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19 (sequence A000961 in the OEIS). 1 is sometimes included.
• An Achilles number is powerful but not a perfect power. The first: 72, 108, 200, 288, 392, 432, 500, 648, 675, 800, 864, 968 (sequence A052486 in the OEIS).
• A square-free integer has no prime factor with multiplicity above 1. The first: 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17 (sequence A005117 in the 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, 102, 105, 110, 114, 130, 138, 154 (sequence A007304 in the 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, 714, 948, 1330, 1520, 1862, 2491, 3248 (sequence A039752 in the OEIS). Another definition is where the same prime is only counted once; if so, the first (by x value): 5, 24, 49, 77, 104, 153, 369, 492, 714, 1682, 2107, 2299 (sequence A006145 in the OEIS).
• A primorial x# is the product of all primes from 2 to x. The first: 2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, 6469693230, 200560490130, 7420738134810 (sequence A002110 in the 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, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600 (sequence A000142 in the OEIS). 0! = 1 is sometimes included.
• A k-smooth number (for a natural number k) has its prime factors ≤ 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, 9, 10, 12, 15, 16 (sequence A051037 in the OEIS).
• A k-powersmooth number has all p ≤ k 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 the tables below with multiplicities above 1 as exponents). The first in decimal: 125, 128, 243, 256, 343, 512, 625, 729, 1024, 1029, 1215, 1250 (sequence A046759 in the OEIS).
• An equidigital number has the same number of digits as its prime factorization. The first in decimal: 1, 2, 3, 5, 7, 10, 11, 13, 14, 15, 16, 17 (sequence A046758 in the OEIS).
• An extravagant number has fewer digits than its prime factorization. The first in decimal: 4, 6, 8, 9, 12, 18, 20, 22, 24, 26, 28, 30 (sequence A046760 in the 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 computing gcd and lcm using 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 − 20 1 2 2 3 3 4 2 5 5 6 2·3 7 7 8 2 9 3 10 2·5 11 11 12 2·3 13 13 14 2·7 15 3·5 16 2 17 17 18 2·3 19 19 20 2·5

21 − 40 21 3·7 22 2·11 23 23 24 2·3 25 5 26 2·13 27 3 28 2·7 29 29 30 2·3·5 31 31 32 2 33 3·11 34 2·17 35 5·7 36 2·3 37 37 38 2·19 39 3·13 40 2·5

41 − 60 41 41 42 2·3·7 43 43 44 2·11 45 3·5 46 2·23 47 47 48 2·3 49 7 50 2·5 51 3·17 52 2·13 53 53 54 2·3 55 5·11 56 2·7 57 3·19 58 2·29 59 59 60 2·3·5

61 − 80 61 61 62 2·31 63 3·7 64 2 65 5·13 66 2·3·11 67 67 68 2·17 69 3·23 70 2·5·7 71 71 72 2·3 73 73 74 2·37 75 3·5 76 2·19 77 7·11 78 2·3·13 79 79 80 2·5

81 − 100 81 3 82 2·41 83 83 84 2·3·7 85 5·17 86 2·43 87 3·29 88 2·11 89 89 90 2·3·5 91 7·13 92 2·23 93 3·31 94 2·47 95 5·19 96 2·3 97 97 98 2·7 99 3·11 100 2·5

101 − 120 101 101 102 2·3·17 103 103 104 2·13 105 3·5·7 106 2·53 107 107 108 2·3 109 109 110 2·5·11 111 3·37 112 2·7 113 113 114 2·3·19 115 5·23 116 2·29 117 3·13 118 2·59 119 7·17 120 2·3·5

121 − 140 121 11 122 2·61 123 3·41 124 2·31 125 5 126 2·3·7 127 127 128 2 129 3·43 130 2·5·13 131 131 132 2·3·11 133 7·19 134 2·67 135 3·5 136 2·17 137 137 138 2·3·23 139 139 140 2·5·7

141 − 160 141 3·47 142 2·71 143 11·13 144 2·3 145 5·29 146 2·73 147 3·7 148 2·37 149 149 150 2·3·5 151 151 152 2·19 153 3·17 154 2·7·11 155 5·31 156 2·3·13 157 157 158 2·79 159 3·53 160 2·5

161 − 180 161 7·23 162 2·3 163 163 164 2·41 165 3·5·11 166 2·83 167 167 168 2·3·7 169 13 170 2·5·17 171 3·19 172 2·43 173 173 174 2·3·29 175 5·7 176 2·11 177 3·59 178 2·89 179 179 180 2·3·5

181 − 200 181 181 182 2·7·13 183 3·61 184 2·23 185 5·37 186 2·3·31 187 11·17 188 2·47 189 3·7 190 2·5·19 191 191 192 2·3 193 193 194 2·97 195 3·5·13 196 2·7 197 197 198 2·3·11 199 199 200 2·5

201 − 220 201 3·67 202 2·101 203 7·29 204 2·3·17 205 5·41 206 2·103 207 3·23 208 2·13 209 11·19 210 2·3·5·7 211 211 212 2·53 213 3·71 214 2·107 215 5·43 216 2·3 217 7·31 218 2·109 219 3·73 220 2·5·11

221 − 240 221 13·17 222 2·3·37 223 223 224 2·7 225 3·5 226 2·113 227 227 228 2·3·19 229 229 230 2·5·23 231 3·7·11 232 2·29 233 233 234 2·3·13 235 5·47 236 2·59 237 3·79 238 2·7·17 239 239 240 2·3·5

241 − 260 241 241 242 2·11 243 3 244 2·61 245 5·7 246 2·3·41 247 13·19 248 2·31 249 3·83 250 2·5 251 251 252 2·3·7 253 11·23 254 2·127 255 3·5·17 256 2 257 257 258 2·3·43 259 7·37 260 2·5·13

261 − 280 261 3·29 262 2·131 263 263 264 2·3·11 265 5·53 266 2·7·19 267 3·89 268 2·67 269 269 270 2·3·5 271 271 272 2·17 273 3·7·13 274 2·137 275 5·11 276 2·3·23 277 277 278 2·139 279 3·31 280 2·5·7

281 − 300 281 281 282 2·3·47 283 283 284 2·71 285 3·5·19 286 2·11·13 287 7·41 288 2·3 289 17 290 2·5·29 291 3·97 292 2·73 293 293 294 2·3·7 295 5·59 296 2·37 297 3·11 298 2·149 299 13·23 300 2·3·5

301 − 320 301 7·43 302 2·151 303 3·101 304 2·19 305 5·61 306 2·3·17 307 307 308 2·7·11 309 3·103 310 2·5·31 311 311 312 2·3·13 313 313 314 2·157 315 3·5·7 316 2·79 317 317 318 2·3·53 319 11·29 320 2·5

321 − 340 321 3·107 322 2·7·23 323 17·19 324 2·3 325 5·13 326 2·163 327 3·109 328 2·41 329 7·47 330 2·3·5·11 331 331 332 2·83 333 3·37 334 2·167 335 5·67 336 2·3·7 337 337 338 2·13 339 3·113 340 2·5·17

341 − 360 341 11·31 342 2·3·19 343 7 344 2·43 345 3·5·23 346 2·173 347 347 348 2·3·29 349 349 350 2·5·7 351 3·13 352 2·11 353 353 354 2·3·59 355 5·71 356 2·89 357 3·7·17 358 2·179 359 359 360 2·3·5

361 − 380 361 19 362 2·181 363 3·11 364 2·7·13 365 5·73 366 2·3·61 367 367 368 2·23 369 3·41 370 2·5·37 371 7·53 372 2·3·31 373 373 374 2·11·17 375 3·5 376 2·47 377 13·29 378 2·3·7 379 379 380 2·5·19

381 − 400 381 3·127 382 2·191 383 383 384 2·3 385 5·7·11 386 2·193 387 3·43 388 2·97 389 389 390 2·3·5·13 391 17·23 392 2·7 393 3·131 394 2·197 395 5·79 396 2·3·11 397 397 398 2·199 399 3·7·19 400 2·5

401 − 420 401 401 402 2·3·67 403 13·31 404 2·101 405 3·5 406 2·7·29 407 11·37 408 2·3·17 409 409 410 2·5·41 411 3·137 412 2·103 413 7·59 414 2·3·23 415 5·83 416 2·13 417 3·139 418 2·11·19 419 419 420 2·3·5·7

421 − 440 421 421 422 2·211 423 3·47 424 2·53 425 5·17 426 2·3·71 427 7·61 428 2·107 429 3·11·13 430 2·5·43 431 431 432 2·3 433 433 434 2·7·31 435 3·5·29 436 2·109 437 19·23 438 2·3·73 439 439 440 2·5·11

441 − 460 441 3·7 442 2·13·17 443 443 444 2·3·37 445 5·89 446 2·223 447 3·149 448 2·7 449 449 450 2·3·5 451 11·41 452 2·113 453 3·151 454 2·227 455 5·7·13 456 2·3·19 457 457 458 2·229 459 3·17 460 2·5·23

461 − 480 461 461 462 2·3·7·11 463 463 464 2·29 465 3·5·31 466 2·233 467 467 468 2·3·13 469 7·67 470 2·5·47 471 3·157 472 2·59 473 11·43 474 2·3·79 475 5·19 476 2·7·17 477 3·53 478 2·239 479 479 480 2·3·5

481 − 500 481 13·37 482 2·241 483 3·7·23 484 2·11 485 5·97 486 2·3 487 487 488 2·61 489 3·163 490 2·5·7 491 491 492 2·3·41 493 17·29 494 2·13·19 495 3·5·11 496 2·31 497 7·71 498 2·3·83 499 499 500 2·5

501 − 520 501 3·167 502 2·251 503 503 504 2·3·7 505 5·101 506 2·11·23 507 3·13 508 2·127 509 509 510 2·3·5·17 511 7·73 512 2 513 3·19 514 2·257 515 5·103 516 2·3·43 517 11·47 518 2·7·37 519 3·173 520 2·5·13

521 − 540 521 521 522 2·3·29 523 523 524 2·131 525 3·5·7 526 2·263 527 17·31 528 2·3·11 529 23 530 2·5·53 531 3·59 532 2·7·19 533 13·41 534 2·3·89 535 5·107 536 2·67 537 3·179 538 2·269 539 7·11 540 2·3·5

541 − 560 541 541 542 2·271 543 3·181 544 2·17 545 5·109 546 2·3·7·13 547 547 548 2·137 549 3·61 550 2·5·11 551 19·29 552 2·3·23 553 7·79 554 2·277 555 3·5·37 556 2·139 557 557 558 2·3·31 559 13·43 560 2·5·7

561 − 580 561 3·11·17 562 2·281 563 563 564 2·3·47 565 5·113 566 2·283 567 3·7 568 2·71 569 569 570 2·3·5·19 571 571 572 2·11·13 573 3·191 574 2·7·41 575 5·23 576 2·3 577 577 578 2·17 579 3·193 580 2·5·29

581 − 600 581 7·83 582 2·3·97 583 11·53 584 2·73 585 3·5·13 586 2·293 587 587 588 2·3·7 589 19·31 590 2·5·59 591 3·197 592 2·37 593 593 594 2·3·11 595 5·7·17 596 2·149 597 3·199 598 2·13·23 599 599 600 2·3·5

601 − 620 601 601 602 2·7·43 603 3·67 604 2·151 605 5·11 606 2·3·101 607 607 608 2·19 609 3·7·29 610 2·5·61 611 13·47 612 2·3·17 613 613 614 2·307 615 3·5·41 616 2·7·11 617 617 618 2·3·103 619 619 620 2·5·31

621 − 640 621 3·23 622 2·311 623 7·89 624 2·3·13 625 5 626 2·313 627 3·11·19 628 2·157 629 17·37 630 2·3·5·7 631 631 632 2·79 633 3·211 634 2·317 635 5·127 636 2·3·53 637 7·13 638 2·11·29 639 3·71 640 2·5

641 − 660 641 641 642 2·3·107 643 643 644 2·7·23 645 3·5·43 646 2·17·19 647 647 648 2·3 649 11·59 650 2·5·13 651 3·7·31 652 2·163 653 653 654 2·3·109 655 5·131 656 2·41 657 3·73 658 2·7·47 659 659 660 2·3·5·11

661 − 680 661 661 662 2·331 663 3·13·17 664 2·83 665 5·7·19 666 2·3·37 667 23·29 668 2·167 669 3·223 670 2·5·67 671 11·61 672 2·3·7 673 673 674 2·337 675 3·5 676 2·13 677 677 678 2·3·113 679 7·97 680 2·5·17

681 − 700 681 3·227 682 2·11·31 683 683 684 2·3·19 685 5·137 686 2·7 687 3·229 688 2·43 689 13·53 690 2·3·5·23 691 691 692 2·173 693 3·7·11 694 2·347 695 5·139 696 2·3·29 697 17·41 698 2·349 699 3·233 700 2·5·7

701 − 720 701 701 702 2·3·13 703 19·37 704 2·11 705 3·5·47 706 2·353 707 7·101 708 2·3·59 709 709 710 2·5·71 711 3·79 712 2·89 713 23·31 714 2·3·7·17 715 5·11·13 716 2·179 717 3·239 718 2·359 719 719 720 2·3·5

721 − 740 721 7·103 722 2·19 723 3·241 724 2·181 725 5·29 726 2·3·11 727 727 728 2·7·13 729 3 730 2·5·73 731 17·43 732 2·3·61 733 733 734 2·367 735 3·5·7 736 2·23 737 11·67 738 2·3·41 739 739 740 2·5·37

741 − 760 741 3·13·19 742 2·7·53 743 743 744 2·3·31 745 5·149 746 2·373 747 3·83 748 2·11·17 749 7·107 750 2·3·5 751 751 752 2·47 753 3·251 754 2·13·29 755 5·151 756 2·3·7 757 757 758 2·379 759 3·11·23 760 2·5·19

761 − 780 761 761 762 2·3·127 763 7·109 764 2·191 765 3·5·17 766 2·383 767 13·59 768 2·3 769 769 770 2·5·7·11 771 3·257 772 2·193 773 773 774 2·3·43 775 5·31 776 2·97 777 3·7·37 778 2·389 779 19·41 780 2·3·5·13

781 − 800 781 11·71 782 2·17·23 783 3·29 784 2·7 785 5·157 786 2·3·131 787 787 788 2·197 789 3·263 790 2·5·79 791 7·113 792 2·3·11 793 13·61 794 2·397 795 3·5·53 796 2·199 797 797 798 2·3·7·19 799 17·47 800 2·5

801 - 820 801 3·89 802 2·401 803 11·73 804 2·3·67 805 5·7·23 806 2·13·31 807 3·269 808 2·101 809 809 810 2·3·5 811 811 812 2·7·29 813 3·271 814 2·11·37 815 5·163 816 2·3·17 817 19·43 818 2·409 819 3·7·13 820 2·5·41

821 - 840 821 821 822 2·3·137 823 823 824 2·103 825 3·5·11 826 2·7·59 827 827 828 2·3·23 829 829 830 2·5·83 831 3·277 832 2·13 833 7·17 834 2·3·139 835 5·167 836 2·11·19 837 3·31 838 2·419 839 839 840 2·3·5·7

841 - 860 841 29 842 2·421 843 3·281 844 2·211 845 5·13 846 2·3·47 847 7·11 848 2·53 849 3·283 850 2·5·17 851 23·37 852 2·3·71 853 853 854 2·7·61 855 3·5·19 856 2·107 857 857 858 2·3·11·13 859 859 860 2·5·43

861 - 880 861 3·7·41 862 2·431 863 863 864 2·3 865 5·173 866 2·433 867 3·17 868 2·7·31 869 11·79 870 2·3·5·29 871 13·67 872 2·109 873 3·97 874 2·19·23 875 5·7 876 2·3·73 877 877 878 2·439 879 3·293 880 2·5·11

881 - 900 881 881 882 2·3·7 883 883 884 2·13·17 885 3·5·59 886 2·443 887 887 888 2·3·37 889 7·127 890 2·5·89 891 3·11 892 2·223 893 19·47 894 2·3·149 895 5·179 896 2·7 897 3·13·23 898 2·449 899 29·31 900 2·3·5

901 - 920 901 17·53 902 2·11·41 903 3·7·43 904 2·113 905 5·181 906 2·3·151 907 907 908 2·227 909 3·101 910 2·5·7·13 911 911 912 2·3·19 913 11·83 914 2·457 915 3·5·61 916 2·229 917 7·131 918 2·3·17 919 919 920 2·5·23

921 - 940 921 3·307 922 2·461 923 13·71 924 2·3·7·11 925 5·37 926 2·463 927 3·103 928 2·29 929 929 930 2·3·5·31 931 7·19 932 2·233 933 3·311 934 2·467 935 5·11·17 936 2·3·13 937 937 938 2·7·67 939 3·313 940 2·5·47

941 - 960 941 941 942 2·3·157 943 23·41 944 2·59 945 3·5·7 946 2·11·43 947 947 948 2·3·79 949 13·73 950 2·5·19 951 3·317 952 2·7·17 953 953 954 2·3·53 955 5·191 956 2·239 957 3·11·29 958 2·479 959 7·137 960 2·3·5

961 - 980 961 31 962 2·13·37 963 3·107 964 2·241 965 5·193 966 2·3·7·23 967 967 968 2·11 969 3·17·19 970 2·5·97 971 971 972 2·3 973 7·139 974 2·487 975 3·5·13 976 2·61 977 977 978 2·3·163 979 11·89 980 2·5·7

981 - 1000 981 3·109 982 2·491 983 983 984 2·3·41 985 5·197 986 2·17·29 987 3·7·47 988 2·13·19 989 23·43 990 2·3·5·11 991 991 992 2·31 993 3·331 994 2·7·71 995 5·199 996 2·3·83 997 997 998 2·499 999 3·37 1000 2·5

• Fundamental theorem of arithmetic – Integers have unique prime factorizations
• List of prime numbers
• Table of divisors