Ken Ward's Mathematics
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Number Theory Table of Divisibility Rules for Numbers Relatively Prime to 10
See Divisibility tests 2
| Number | Plus Factor | Minus Factor |
|---|
| 3 | 1 | 2 |
| 7 | 5 | 2 |
| 9 | 1 | 8 |
| 11 | 10 | 1 |
| 13 | 4 | 9 |
| 15 | None | None |
| 17 | 12 | 5 |
| 19 | 2 | 17 |
| 21 | 19 | 2 |
| 23 | 7 | 16 |
| 25 | None | None |
| 27 | 19 | 8 |
| 29 | 3 | 26 |
| 31 | 28 | 3 |
| 33 | 10 | 23 |
| 35 | None | None |
| 37 | 26 | 26 |
| 39 | 4 | 35 |
| 41 | 37 | 4 |
| 43 | 13 | 30 |
| 45 | None | None |
| 47 | 33 | 33 |
| 49 | 5 | 44 |
| 51 | 46 | 5 |
| 53 | 16 | 37 |
| 55 | None | None |
| 57 | 40 | 40 |
| 59 | 6 | 53 |
| 61 | 55 | 6 |
| 63 | 19 | 44 |
| 65 | None | None |
| 67 | 47 | 47 |
| 69 | 7 | 62 |
| 71 | 64 | 7 |
| 73 | 22 | 51 |
| 75 | None | None |
| 77 | 54 | 54 |
| 79 | 8 | 71 |
| 81 | 73 | 8 |
| 83 | 25 | 58 |
| 85 | None | None |
| 87 | 61 | 61 |
| 89 | 9 | 80 |
| 91 | 82 | 9 |
| 93 | 28 | 65 |
| 95 | None | None |
| 97 | 68 | 68 |
| 99 | 10 | 89 |
| 101 | 91 | 10 |
| 103 | 31 | 72 |
| 105 | None | None |
| 107 | 75 | 75 |
| 109 | 11 | 98 |
| 111 | 100 | 100 |
| 113 | 34 | 79 |
| 115 | None | None |
| 117 | 82 | 82 |
| 119 | 12 | 107 |
| 121 | 109 | 109 |
| 123 | 37 | 86 |
| 125 | None | None |
| 127 | 89 | 89 |
| 129 | 13 | 116 |
| 131 | 118 | 118 |
| 133 | 40 | 93 |
| 135 | None | None |
| 137 | 96 | 96 |
| 139 | 14 | 125 |
| 141 | 127 | 127 |
| 143 | 43 | 100 |
| 145 | None | None |
| 147 | 103 | 103 |
| 149 | 15 | 134 |
| 151 | 136 | 136 |
| 153 | 46 | 107 |
| 155 | None | None |
| 157 | 110 | 110 |
| 159 | 16 | 143 |
| 161 | 145 | 145 |
| 163 | 49 | 114 |
| 165 | None | None |
| 167 | 117 | 117 |
| 169 | 17 | 152 |
| 171 | 154 | 154 |
| 173 | 52 | 121 |
| 175 | None | None |
| 177 | 124 | 124 |
| 179 | 18 | 161 |
| 181 | 163 | 163 |
| 183 | 55 | 128 |
| 185 | None | None |
| 187 | 131 | 131 |
| 189 | 19 | 170 |
| 191 | 172 | 172 |
| 193 | 58 | 135 |
| 195 | None | None |
| 197 | 138 | 138 |
| 199 | 20 | 179 |
| 201 | 181 | 181 |
| 203 | 61 | 142 |
| 205 | None | None |
| 207 | 145 | 145 |
| 209 | 21 | 188 |
| 211 | 190 | 190 |
| 213 | 64 | 149 |
| 215 | None | None |
| 217 | 152 | 152 |
| 219 | 22 | 197 |
| 221 | 199 | 199 |
| 223 | 67 | 156 |
| 225 | None | None |
| 227 | 159 | 159 |
| 229 | 23 | 206 |
| 231 | 208 | 208 |
| 233 | 70 | 163 |
| 235 | None | None |
| 237 | 166 | 166 |
| 239 | 24 | 215 |
| 241 | 217 | 217 |
| 243 | 73 | 170 |
| 245 | None | None |
| 247 | 173 | 173 |
| 249 | 25 | 224 |
| 251 | 226 | 226 |
| 253 | 76 | 177 |
| 255 | None | None |
| 257 | 180 | 180 |
| 259 | 26 | 233 |
| 261 | 235 | 235 |
| 263 | 79 | 184 |
| 265 | None | None |
| 267 | 187 | 187 |
| 269 | 27 | 242 |
| 271 | 244 | 244 |
| 273 | 82 | 191 |
| 275 | None | None |
| 277 | 194 | 194 |
| 279 | 28 | 251 |
| 281 | 253 | 253 |
| 283 | 85 | 198 |
| 285 | None | None |
| 287 | 201 | 201 |
| 289 | 29 | 260 |
| 291 | 262 | 262 |
| 293 | 88 | 205 |
| 295 | None | None |
| 297 | 208 | 208 |
| 299 | 30 | 269 |
| 301 | 271 | 271 |
| 303 | 91 | 212 |
| 305 | None | None |
| 307 | 215 | 215 |
| 309 | 31 | 278 |
| 311 | 280 | 280 |
| 313 | 94 | 219 |
| 315 | None | None |
| 317 | 222 | 222 |
| 319 | 32 | 287 |
| 321 | 289 | 289 |
| 323 | 97 | 226 |
| 325 | None | None |
| 327 | 229 | 229 |
| 329 | 33 | 296 |
| 331 | 298 | 298 |
| 333 | 100 | 233 |
| 335 | None | None |
| 337 | 236 | 236 |
| 339 | 34 | 305 |
| 341 | 307 | 307 |
| 343 | 103 | 240 |
| 345 | None | None |
| 347 | 243 | 243 |
| 349 | 35 | 314 |
| 351 | 316 | 316 |
| 353 | 106 | 247 |
| 355 | None | None |
| 357 | 250 | 250 |
| 359 | 36 | 323 |
| 361 | 325 | 325 |
| 363 | 109 | 254 |
| 365 | None | None |
| 367 | 257 | 257 |
| 369 | 37 | 332 |
| 371 | 334 | 334 |
| 373 | 112 | 261 |
| 375 | None | None |
| 377 | 264 | 264 |
| 379 | 38 | 341 |
| 381 | 343 | 343 |
| 383 | 115 | 268 |
| 385 | None | None |
| 387 | 271 | 271 |
| 389 | 39 | 350 |
| 391 | 352 | 352 |
| 393 | 118 | 275 |
| 395 | None | None |
| 397 | 278 | 278 |
| 399 | 40 | 359 |
| 401 | 361 | 361 |
| 403 | 121 | 282 |
| 405 | None | None |
| 407 | 285 | 285 |
| 409 | 41 | 368 |
| 411 | 370 | 370 |
| 413 | 124 | 289 |
| 415 | None | None |
| 417 | 292 | 292 |
| 419 | 42 | 377 |
| 421 | 379 | 379 |
| 423 | 127 | 296 |
| 425 | None | None |
| 427 | 299 | 299 |
| 429 | 43 | 386 |
| 431 | 388 | 388 |
| 433 | 130 | 303 |
| 435 | None | None |
| 437 | 306 | 306 |
| 439 | 44 | 395 |
| 441 | 397 | 397 |
| 443 | 133 | 310 |
| 445 | None | None |
| 447 | 313 | 313 |
| 449 | 45 | 404 |
| 451 | 406 | 406 |
| 453 | 136 | 317 |
| 455 | None | None |
| 457 | 320 | 320 |
| 459 | 46 | 413 |
| 461 | 415 | 415 |
| 463 | 139 | 324 |
| 465 | None | None |
| 467 | 327 | 327 |
| 469 | 47 | 422 |
| 471 | 424 | 424 |
| 473 | 142 | 331 |
| 475 | None | None |
| 477 | 334 | 334 |
| 479 | 48 | 431 |
| 481 | 433 | 433 |
| 483 | 145 | 338 |
| 485 | None | None |
| 487 | 341 | 341 |
| 489 | 49 | 440 |
| 491 | 442 | 442 |
| 493 | 148 | 345 |
| 495 | None | None |
| 497 | 348 | 348 |
| 499 | 50 | 449 |
| 501 | 451 | 451 |
| 503 | 151 | 352 |
| 505 | None | None |
| 507 | 355 | 355 |
| 509 | 51 | 458 |
| 511 | 460 | 460 |
| 513 | 154 | 359 |
| 515 | None | None |
| 517 | 362 | 362 |
| 519 | 52 | 467 |
| 521 | 469 | 469 |
| 523 | 157 | 366 |
| 525 | None | None |
| 527 | 369 | 369 |
| 529 | 53 | 476 |
| 531 | 478 | 478 |
| 533 | 160 | 373 |
| 535 | None | None |
| 537 | 376 | 376 |
| 539 | 54 | 485 |
| 541 | 487 | 487 |
| 543 | 163 | 380 |
| 545 | None | None |
| 547 | 383 | 383 |
| 549 | 55 | 494 |
| 551 | 496 | 496 |
| 553 | 166 | 387 |
| 555 | None | None |
| 557 | 390 | 390 |
| 559 | 56 | 503 |
| 561 | 505 | 505 |
| 563 | 169 | 394 |
| 565 | None | None |
| 567 | 397 | 397 |
| 569 | 57 | 512 |
| 571 | 514 | 514 |
| 573 | 172 | 401 |
| 575 | None | None |
| 577 | 404 | 404 |
| 579 | 58 | 521 |
| 581 | 523 | 523 |
| 583 | 175 | 408 |
| 585 | None | None |
| 587 | 411 | 411 |
| 589 | 59 | 530 |
| 591 | 532 | 532 |
| 593 | 178 | 415 |
| 595 | None | None |
| 597 | 418 | 418 |
| 599 | 60 | 539 |
| 601 | 541 | 541 |
| 603 | 181 | 422 |
| 605 | None | None |
| 607 | 425 | 425 |
| 609 | 61 | 548 |
| 611 | 550 | 550 |
| 613 | 184 | 429 |
| 615 | None | None |
| 617 | 432 | 432 |
| 619 | 62 | 557 |
| 621 | 559 | 559 |
| 623 | 187 | 436 |
| 625 | None | None |
| 627 | 439 | 439 |
| 629 | 63 | 566 |
| 631 | 568 | 568 |
| 633 | 190 | 443 |
| 635 | None | None |
| 637 | 446 | 446 |
| 639 | 64 | 575 |
| 641 | 577 | 577 |
| 643 | 193 | 450 |
| 645 | None | None |
| 647 | 453 | 453 |
| 649 | 65 | 584 |
| 651 | 586 | 586 |
| 653 | 196 | 457 |
| 655 | None | None |
| 657 | 460 | 460 |
| 659 | 66 | 593 |
| 661 | 595 | 595 |
| 663 | 199 | 464 |
| 665 | None | None |
| 667 | 467 | 467 |
| 669 | 67 | 602 |
| 671 | 604 | 604 |
| 673 | 202 | 471 |
| 675 | None | None |
| 677 | 474 | 474 |
| 679 | 68 | 611 |
| 681 | 613 | 613 |
| 683 | 205 | 478 |
| 685 | None | None |
| 687 | 481 | 481 |
| 689 | 69 | 620 |
| 691 | 622 | 622 |
| 693 | 208 | 485 |
| 695 | None | None |
| 697 | 488 | 488 |
| 699 | 70 | 629 |
| 701 | 631 | 631 |
| 703 | 211 | 492 |
| 705 | None | None |
| 707 | 495 | 495 |
| 709 | 71 | 638 |
| 711 | 640 | 640 |
| 713 | 214 | 499 |
| 715 | None | None |
| 717 | 502 | 502 |
| 719 | 72 | 647 |
| 721 | 649 | 649 |
| 723 | 217 | 506 |
| 725 | None | None |
| 727 | 509 | 509 |
| 729 | 73 | 656 |
| 731 | 658 | 658 |
| 733 | 220 | 513 |
| 735 | None | None |
| 737 | 516 | 516 |
| 739 | 74 | 665 |
| 741 | 667 | 667 |
| 743 | 223 | 520 |
| 745 | None | None |
| 747 | 523 | 523 |
| 749 | 75 | 674 |
| 751 | 676 | 676 |
| 753 | 226 | 527 |
| 755 | None | None |
| 757 | 530 | 530 |
| 759 | 76 | 683 |
| 761 | 685 | 685 |
| 763 | 229 | 534 |
| 765 | None | None |
| 767 | 537 | 537 |
| 769 | 77 | 692 |
| 771 | 694 | 694 |
| 773 | 232 | 541 |
| 775 | None | None |
| 777 | 544 | 544 |
| 779 | 78 | 701 |
| 781 | 703 | 703 |
| 783 | 235 | 548 |
| 785 | None | None |
| 787 | 551 | 551 |
| 789 | 79 | 710 |
| 791 | 712 | 712 |
| 793 | 238 | 555 |
| 795 | None | None |
| 797 | 558 | 558 |
| 799 | 80 | 719 |
| 801 | 721 | 721 |
| 803 | 241 | 562 |
| 805 | None | None |
| 807 | 565 | 565 |
| 809 | 81 | 728 |
| 811 | 730 | 730 |
| 813 | 244 | 569 |
| 815 | None | None |
| 817 | 572 | 572 |
| 819 | 82 | 737 |
| 821 | 739 | 739 |
| 823 | 247 | 576 |
| 825 | None | None |
| 827 | 579 | 579 |
| 829 | 83 | 746 |
| 831 | 748 | 748 |
| 833 | 250 | 583 |
| 835 | None | None |
| 837 | 586 | 586 |
| 839 | 84 | 755 |
| 841 | 757 | 757 |
| 843 | 253 | 590 |
| 845 | None | None |
| 847 | 593 | 593 |
| 849 | 85 | 764 |
| 851 | 766 | 766 |
| 853 | 256 | 597 |
| 855 | None | None |
| 857 | 600 | 600 |
| 859 | 86 | 773 |
| 861 | 775 | 775 |
| 863 | 259 | 604 |
| 865 | None | None |
| 867 | 607 | 607 |
| 869 | 87 | 782 |
| 871 | 784 | 784 |
| 873 | 262 | 611 |
| 875 | None | None |
| 877 | 614 | 614 |
| 879 | 88 | 791 |
| 881 | 793 | 793 |
| 883 | 265 | 618 |
| 885 | None | None |
| 887 | 621 | 621 |
| 889 | 89 | 800 |
| 891 | 802 | 802 |
| 893 | 268 | 625 |
| 895 | None | None |
| 897 | 628 | 628 |
| 899 | 90 | 809 |
| 901 | 811 | 811 |
| 903 | 271 | 632 |
| 905 | None | None |
| 907 | 635 | 635 |
| 909 | 91 | 818 |
| 911 | 820 | 820 |
| 913 | 274 | 639 |
| 915 | None | None |
| 917 | 642 | 642 |
| 919 | 92 | 827 |
| 921 | 829 | 829 |
| 923 | 277 | 646 |
| 925 | None | None |
| 927 | 649 | 649 |
| 929 | 93 | 836 |
| 931 | 838 | 838 |
| 933 | 280 | 653 |
| 935 | None | None |
| 937 | 656 | 656 |
| 939 | 94 | 845 |
| 941 | 847 | 847 |
| 943 | 283 | 660 |
| 945 | None | None |
| 947 | 663 | 663 |
| 949 | 95 | 854 |
| 951 | 856 | 856 |
| 953 | 286 | 667 |
| 955 | None | None |
| 957 | 670 | 670 |
| 959 | 96 | 863 |
| 961 | 865 | 865 |
| 963 | 289 | 674 |
| 965 | None | None |
| 967 | 677 | 677 |
| 969 | 97 | 872 |
| 971 | 874 | 874 |
| 973 | 292 | 681 |
| 975 | None | None |
| 977 | 684 | 684 |
| 979 | 98 | 881 |
| 981 | 883 | 883 |
| 983 | 295 | 688 |
| 985 | None | None |
| 987 | 691 | 691 |
| 989 | 99 | 890 |
| 991 | 892 | 892 |
| 993 | 298 | 695 |
| 995 | None | None |
| 997 | 698 | 698 |
| 999 | 100 | 899 |
Ken Ward's Mathematics Pages