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The remainder when the sum of 0! + 1! + 2! +.....+ 99! + 100! is divided by 12 is

The remainder when the sum of 0! + 1! + 2! +.....+ 99! + 100! is divided by 12 is Correct Answer 10

Calculation:

Given sum is
0! + 1! + 2! +.....+ 99! + 100!

As we can see, all factorials except 0!, 1!, 2!, 3! has the product of 4 & 3 in their factor so, they are completely divisible by 12. 

Therefore, we consider only on the sum of 0! + 1! + 2! + 3!

⇒ Sum = 1 + 1 + 2 + 6

⇒ Sum = 10

Which when divided by 12 leaves remainder as 10.

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