When 53 is divided by a positive integer n ,the remainder is 3 .How many values of n are possible?

题目

When 53 is divided by a positive integer n ,the remainder is 3 .How many values of n are possible?
THE ANSWER IS 4,BUT WHYYYYYYYY?

答案

首先,n>3,否则余数不能为3；
其次,n整除(53-3),即n整除50；
所以,n=5,10,25,50；
有四种可能.