1-Number Numbers

Number Theory Level pending

The smallest positive integer that have digits which are all the same and is a multiple of 49 49 can be expressed as a a what is the value of a 49 \frac{a}{49} ?

The answer is 15873.

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1 solution

Ephram Chun
Jan 26, 2021

We realize that 49 = 7 2 49=7^2 thus if we find a number that has all the digits which are the same and is divisible by 7 7 we can multiply that by 7 7 and it will still have all the same digits. Thus by inspection we see that 111111 111111 is divisible by 7 7 thus our answer is 7 111111 49 = 15873 \frac{7*111111}{49}=\boxed{15873}

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