Can three go into 564

Answer 1

Yes. It goes in 188 times.

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To be divisible by 3, sum the digits of the number and if this sum is divisible by 3, then the original number is divisible by 3.

As the test can be repeated on the sum, repeat the summing until a single digit remains; only if this number is one of {3, 6, 9} is the original number divisible by 3.

For 564 this gives:

564 → 5 + 6 + 4 = 15

15 → 1 + 5 = 6

6 is one of {3, 6,9} so 564 is divisible by 3.