Want to know if a big number divides evenly by 3 or 9, without doing the division?

🪄 The trick: Add up the digits. If the digit sum divides by 3, so does the number. If it divides by 9, so does the number.

Example 1: 4572

4 + 5 + 7 + 2 = 18

18 divides by 9 (and by 3)

4572 divides by 9 and by 3

Example 2: 1234

1 + 2 + 3 + 4 = 10

10 does not divide by 3

1234 does not divide by 3 or 9

Why it works

Every power of 10 is one more than a multiple of 9 (10 = 9 + 1, 100 = 99 + 1, …). So a number and its digit sum always leave the same remainder when divided by 9, and by 3.

Your turn

  1. Does 7461 divide by 9?
    Show answer

    7 + 4 + 6 + 1 = 18, so yes

  2. Does 5203 divide by 3?
    Show answer

    5 + 2 + 0 + 3 = 10, so no

  3. Does 111 111 divide by 3?
    Show answer

    The digit sum is 6, so yes

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