Question

Find the remainder when 1!+2!+3!+...+15! is divided by 15

Answer 1

• 3

Explanation:

We know that

• n! = 1*2*3*...*n

We also know that

• 15 = 3*5

Since 5! = 1*2*3*4*5 is divisible by 15:

• any n! with n ≥ 5 is divisible by 15.

We need to find the remainder when 1! + 2! + 3! + 4! is divided by 15 as all the rest are divisible by 15.

The sum is:

• 1! + 2! + 3! + 4! = 1 + 2 + 6 + 24 = 33

The remainder is:

• 33/15 = 2 rem 3

As we see the remainder is 3