<p>when 53 is divided by a positive integer n, the remainder is 3, how many possible values of n are there? i know the answer is 4, and values of n are 50,25,10,5. I was wondering if there is a mathematical way of solving this without doing trail and errors.</p>
<p>This means that 50 leaves remainder 0 when divided by n (with exceptions, I’ll show later). Since 50 = (2^1)(5^2), there are (1+1)(2+1) = 6 positive factors of 50.</p>
<p>However we can’t include 1 and 2, since the remainder wouldn’t be 3. So what you really want are the factors of 50 that are greater than 3, in which there are four.</p>