Question

What is the remainder when 1! + 2! + 3! + 4! ........2006! Is divided by 21?​

Answer 1

Answer:

14

Step-by-step explanation:

Pls refer to the attachment for the detailed solution.

Answer 2

The remainder is 34.

Step-by-step explanation:

Since we have given that

$1!+2!+3!+4!+...............+2006!$

We need to find the remainder in which it is divisible by 21.

So, after 7! onwards all are divisible by 21.

So, we need to check from 1! to 6! only.

Remainder of 1! when divided by 21 = 1

Remainder of 2! when divided by 21 = 2

Remainder of 3! when divided by 21 = 6

Remainder of 4! when divided by 21 = 3

Remainder of 5! when divided by 21 = 15

Remainder of 6! when divided by 21 = 7

So, the remainder would be

$1+2+6+3+15+7=34$

Hence, the remainder is 34.

# learn more:

Find 1!+2!+3!+4!+.........+2006!

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