Multiple of 15

Determine the smallest positive multiple of 15 that consists solely of the digits 1 and 0.

Answer


For a number to be divisible by 15 it must be divisible by both 3 and 5. Divisibility by 5 means the last digit must be a 0 or a 5; in our case this forces the last digit to be 0. Divisibility by 3 requires that the sum of the digits is divisible by 3. The smallest number made up only of 1’s and 0’s that meets these conditions is \(\boxed{1110}\).

Notes and comments

Comment 1:
A number is divisible by 3 (or 9) if and only if the sum of its digits is divisible by 3 (or 9).

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