Question 1111525: What is the smallest positive integer that only comprises of the digits 0 and 1, and is a multiple of 42? Answer by ikleyn(52810) (Show Source):
It must be multiple of 3 ====> so it must contain at least three "1" digits.
It must be multiple of 2 ====> so it ends on "0".
Try this:
1110 : is not an integer.
11010 : is not an integer.
10110 : is not an integer.
Next to try is 101010, and it works.
Solved.
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Logic and knowledge of the divisibility rules help you to organize the search by a rational way.
