Quiz 112

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                                                   

 

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). The sum of the digits of a number that is divisible by 3 must equal 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