Dividing Numbers With Consecutive Digits

Most numbers with consecutive digits are divisible by 3! Observe below:

012 ÷ 3 = 4

123 ÷ 3 = 41

234 ÷ 3 = 78

345 ÷ 3 = 115

456 ÷ 3 = 152

567 ÷ 3 = 189

678 ÷ 3 = 226

789 ÷ 3 = 263

[The pattern stops here since 9 is the greatest digit & 890 is NOT divisible by 3]

The number is especially divisible by 3 if the total number of digits is divisible by 3! (Have you noticed the padding zero I put on the number 12?) All the quotients in the example above have an integral difference of 37.

But there's more you can do in this trick! You can skip digits so that only odd or even digits are used, or you can just use 0, 3, 6 & 9 - the single digit multiples of 3. (Yes, zero counts as a multiple, too.)

246 ÷ 3 = 82

468 ÷ 3 = 156

369 ÷ 3 = 123

135 ÷ 3 = 45

123,456 ÷ 3 = 41,152

123,456,789 ÷ 3 = 41,152,263

9,630 ÷ 3 = 3,210

147,741 ÷ 3 = 49,247

If the number of digits isn't divisible by 3 or the digits aren't consecutive, then the whole number isn't divisible by 3.

1,234 ÷ 3 = 411 + 1/3 (Not an integer!)

572 ÷ 3 = 190 + 2/3 (Not an integer!)

There's this special rule for divisibility by 3:

If the sum of all the digits in a number is divisible by 3, then the number itself is also divisible by 3.

This often happens if the number has consecutive digits or the total number of digits is divisible by 3!

It doesn't matter if the consecutive digits are forwards or backwards!

987 ÷ 3 = 329

876 ÷ 3 = 292

765 ÷ 3 = 255

654 ÷ 3 = 218

543 ÷ 3 = 181

432 ÷ 3 = 144

321 ÷ 3 = 107

210 ÷ 3 = 70

[The pattern stops here since 0 is the least digit & 109 is NOT divisible by 3 (In fact, 109 is a prime number!)]

If all of the digits are the same & the total number of digits is divisible by 3, then the number is divisible by 3!

111 ÷ 3 = 37

222 ÷ 3 = 74

333 ÷ 3 = 111

111,111 ÷ 3 = 37,037

444,444,444 ÷ 3 = 148,148,148

555,555,555,555 ÷ 3 = 185,185,185,185

Numbers that are divisible by 3 may also be divisible by 6 or 9...

Back to Index Page Back to Math Trick Menu