How do I solve this problem regarding parity from my Math Challenge class?

Question

The remainder when the product 1492 x 1776 x 1812 x 1996 is divided by 5 is

A. 0

B. 1

C. 2

D. 3

E. 4

*what's the shortcut to figuring out the answer for problems like this?*

Answer 1

In this case, since you are dividing by 5, you only need to need to look at the last digit of each number in this product (1492 x 1776 x 1812 x1996). Thus we get, 2 x 6 x 2 x 6 = 12 x 12 = 144, where the last digit is 4.

This means that the last digit of product (1492 x 1776 x 1812 x1996) is also 4, which is the remainder.

So the answer is E.

*This shortcut works when you are dividing by 5.