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Divisibility rules
Quick tricks for spotting whether a number is divisible by 2, 3, 4, 5, 6, 9 or 10 — without dividing.
Divisibility rules
Type any number — see which rules it passes without doing the long division.
÷2
Ends in 0, 2, 4, 6 or 8
÷3
Sum of digits is divisible by 3
÷4
Last two digits form a multiple of 4
÷5
Ends in 0 or 5
÷6
Divisible by both 2 and 3
÷9
Sum of digits is divisible by 9
÷10
Ends in 0
Why these rules work
The 3 and 9 tricks rely on the fact that 10 ≡ 1 (mod 3) and 10 ≡ 1 (mod 9). So every digit contributes only its face value to the remainder — that's why summing the digits works.
The 2, 4, 5 and 10 rules look only at the last digits because higher place values are already multiples of those numbers (every 100 is a multiple of 4, every 10 is a multiple of 5, etc).