You are given a positive integer such that when the integer is divided by 1995, the remainder is 75. What will the remainder be when the same positive integer is divided by 57?

Question

You are given a positive integer such that when the integer is divided by 1995, the remainder is 75.  What will the remainder be when the same positive integer is divided by 57?

MathMate · Answer

Have you noticed that 57|1995? (reads 57 divides 1995) This means that 1995/57 leaves no remainder. This means that 1995/57 will also leave 75 as a remainder. Since 75 > 57, we will say that the remainder when the original integer is divided by 57 is actually 75-57=18.