Divisible by 3 or 9?

Add up the digits — the answer is hiding in the total.

The question

Is 4,725 divisible by 3 and by 9?

The trick

Add all the digits. If the total divides by 3, so does the number. If the total divides by 9, so does the number.

Worked example

14 + 7 + 2 + 5 = 18
218 divides by 3, so 4,725 divides by 3
318 also divides by 9, so 4,725 divides by 9

So: Yes to both

Remember it like this

Three and nine are nosy — they only care about the digits added up, never the number itself.

In the exam

If the digit sum is still large, add again. 9,999 → 36 → 9. Keep collapsing until you reach a single digit; that digit is your remainder clue.

Why it works

Every power of 10 leaves a remainder of 1 when divided by 9 (10 = 9+1, 100 = 99+1). So a whole number leaves the same remainder as the sum of its digits.

Explain this to my childGet the words to teach it, in your language

Try it yourself

0/4 correct

1
Is 513 divisible by 9? (yes/no)
2
Is 2,346 divisible by 3? (yes/no)
3
Is 1,111 divisible by 3? (yes/no)
4
Is 837 divisible by 9? (yes/no)