Number Puzzle #07- Division By 15 -
Can you find the smallest positive number that is divisible by 15 that consists ONLY of ones
and zeroes (e.g. 10, 11, 100, etc.)? Note that you don't need a calculator to solve the problem.
HINT: If a number is divisible by 15, it must be divisible by both 3 and 5.
ANSWER:
1,110.
EXPLANATION: Because the number is divisible by 15, it must also be divisible by 3 and 5 (since
15 is divisible by 3 and 5). If the sum of the digits of a number is divisible by 3, then the number
itself is divisible by 3 (this is a clever little math trick/shortcut). The number therefore must contain
three ones, six ones, etc. Since the number is divisible by 5, we know that it must end in a 0 (numbers
that are divisible by 5 end in a 0 or a 5). The first number that contains three ones and ends in a 0 is
1,110.
Do you have a
suggestion for this puzzle (e.g. something that should
be mentioned/clarified in the question or solution, bug, typo, etc.)?
