Question

What is the remainder when (1! + 2! + 3!+...1000!) is divided by 5?

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C 3

We know that 5! or greater than 5! will be divisible by 5, Therefore, when (1! + 2! + 3!...1000!) is divisible by 5 equals to when (1! + 2! + 3! + 4!) is divided by 5. we get the remainder as
$\frac{1!+2!+3!+4!}{5}=\frac{33}{5}=\frac{3}{5}$
Hence, remainder obtained = 3