Question

The integers 34041 and 32506, when divided by a three digit integer N, leave the same remainder. What can be the value of N?

Answer 1

Find the difference between both 34041 and 32506.

34041 - 32506 = 1535

So N should be a factor of 1535.

Factors of 1535:-

1, 5, 307, 1535

Here, 307 is a three digit factor of 1535. So N = 307

34041 and 32506 divided by 307 leaves remainder 271.

So 307 is the answer.

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Answer 2

let remainder = x

By euclids division lemma 34041=bn+x:(1)

similarly

32506=an+x:(2)

therefore by subtracting (2) from (1)

1535=(b-a)n

So N should be a factor of 1535.  

Factors of 1535:-  

1, 5, 307, 1535  

Here, 307 is a three digit factor of 1535. So N = 307