Question

When 58123 and 59059 is divided by a three digit number N the remainder comes same. Find the least value of N.

Answer 1

Work is that of @Ravi_Handa
http://tinyurl.com/o5dohrr

We are given that 58123 and 59059 leave the same remainder (let's say 'r') when divided by N. So,
58123 = kN + r
59059 = k'N + r
=> 59059 - 58123 = (k' - k)N
=> (k' - k)N = 936

So, N is a 3-digit factor of 936
936 = 2^3 * 3^2 * 13
Three digit factors are:
936, 936/2, 936/3, 936/4, 936/6, 936/8, and 936/9

There are 7 numbers which satisfy the given property.
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Find the values of these and select the smallest one for your answer:

936, 936/2, 936/3, 936/4, 936/6, 936/8, and 936/9

@JMark