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Term

Harshad / Niven

Numbers divisible by the sum of their decimal digits (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, …).

426 numbers tagged.

A Harshad number (also called a Niven number) is divisible by the sum of its decimal digits. The first Harshad numbers are 1–10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60.

For example, 18 has digit sum 9 and 18 is divisible by 9, so 18 is Harshad. 19 has digit sum 10 but 19 isn't divisible by 10, so 19 is not.

The name was coined by D. R. Kaprekar; harshad means "giver of joy" in Sanskrit. Harshad numbers are base-dependent — a number Harshad in base 10 may not be Harshad in another base. There are infinitely many in any base. All-Harshad numbers (Harshad in every base) are 1, 2, 4, and 6 only.

1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42 45 48 50 54 60 63 70 72 80 81 84 90 100 102 108 110 111 112 114 117 120 126 132 133 135 140 144 150 152 153 156 162 171 180 190 192 195 198 200 201 204 207 209 210 216 220 222 224 225 228 230 234 240 243 247 252 261 264 266 270 280 285 288 300 306 308 312 315 320 322 324 330 333 336 342 351 360 364 370 372 375 378 392 396 399 400 402 405 407 408 410 414 420 423 432 440 441 444 448 450 460 465 468 476 480 481 486 500 504 506 510 511 512 513 516 518 522 531 540 550 552 555 558 576 588 592 594 600 603 605 612 621 624 629 630 640 644 645 648 660 666 684 690 700 702 704 711 715 720 730 732 735 736 738 756 770 774 777 780 782 792 800 801 803 804 810 820 825 828 832 840 846 864 870 874 880 882 888 900 902