Term

Gapful Number

Numbers of 3+ digits divisible by the two-digit number formed by their first and last digit (100, 105, 108, 110, 120, …).

308 numbers tagged.

A gapful number has at least three digits and is divisible by the number formed by its first and last digits — the digits framing the "gap." For example, 192 begins with 1 and ends with 2, and 192 ÷ 12 = 16 exactly, so 192 is gapful.

About 7.5% of all integers are gapful. The term was coined relatively recently (by recreational mathematicians around 2017), making it one of the youngest named number classes on the site.

100 105 108 110 120 121 130 132 135 140 143 150 154 160 165 170 176 180 187 190 192 195 198 200 220 225 231 240 242 253 260 264 275 280 286 297 300 315 330 341 352 360 363 374 385 390 396 400 405 440 451 462 473 480 484 495 500 550 561 572 583 594 600 660 671 682 693 700 770 781 792 800 880 891 900 990 1,000 1,001 1,005 1,008 1,010 1,020 1,030 1,032 1,035 1,037 1,040 1,050 1,053 1,056 1,060 1,064 1,065 1,070 1,080 1,090 1,092 1,095 1,098 1,100 1,110 1,111 1,120 1,125 1,130 1,134 1,136 1,140 1,150 1,152 1,155 1,159 1,160 1,170 1,180 1,183 1,185 1,188 1,190 1,200 1,204 1,207 1,210 1,212 1,215 1,216 1,220 1,221 1,230 1,240 1,245 1,250 1,260 1,270 1,272 1,274 1,275 1,278 1,280 1,290 1,296 1,300 1,305 1,310 1,313 1,320 1,330 1,331 1,332 1,335 1,340 1,344 1,349 1,350 1,360 1,365 1,368 1,370 1,376 1,377 1,380 1,390 1,392 1,395 1,400 1,410 1,414 1,420 1,425 1,430 1,440 1,441 1,443 1,450 1,452 1,455 1,456 1,458 1,460 1,470 1,480 1,484 1,485 1,490 1,500 1,510 1,512 1,515 1,520 1,530 1,536 1,539 1,540 1,545 1,547 1,548 1,550 1,551 1,554 1,560

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