How to Divide by 3 in Your Head

Updated 4 October 2026

First check it divides evenly (digit-sum rule), then chunk through.

5712 ÷ 3 = 1904

How do you divide by 3 in your head?

To divide by 3, first add the digits: if the sum divides by 3, so does the number, and the answer comes out whole. For 5712, the digits give 5 + 7 + 1 + 2 = 15, which divides by 3, so 5712 ÷ 3 is whole. Then work from left to right, one digit at a time. 5 ÷ 3 is 1 remainder 2, so carry the 2 onto the 7 to make 27, and 27 ÷ 3 = 9. The 1 is too small, so write 0 and carry it onto the 2 to make 12, and 12 ÷ 3 = 4. The answer is 1904. The digit sum works because 10, 100 and 1000 each leave remainder 1 when divided by 3, so a number and its digit sum leave the same remainder. When the digit sum does not divide by 3, it still gives the remainder: 5713 has digit sum 16, which leaves 1, so 5713 ÷ 3 is 1904 remainder 1.

1. Check first: the digit sum 15 divides by 3, so 5712 will divide exactly too.

2. 3 into 5 goes 1, remainder 2. Then 3 into 27 goes 9 exactly.

3. 3 into 1 does not go: write 0. Then 3 into 12 goes 4. Quotient: 1904.

All 36 shortcuts: the Magic Tricks library.