Question

The positive number x is divisible by 42, and is composed of only 1s and 0s when written in base 10. what's the smallest number that x might be?

Answer 1

You are given a positive number x that is divisible by 42. You are also given that the answer must be composed of only 1s and 0s when written in base 10. You are asked to find what is the smallest number that x is.

We can solve this through trial and error. I manually multiplied numbers starting from 1 and then multiplied it with 42 to see if I can get a value that has a 1 and a 0. So far, the least number is 5.

5 x 42 = 210

But the question asks for a complete 1s and 0s for the answer, and so, by manual multiplication,

42 x 2,405 = 101,010
or
210 x 481 = 101,010

The least number is 5.