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

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

Mathematics
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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. ----------------- 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

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