Question

find the remainder when 1!+2!+3!+............ +10! is divisible by 6. explain the short cut method to find the remainder​

Answer 1

Answer:

remainder of 55/6 = 1

Step-by-step explanation:

To find the remainder of a number divided by 3, add the digits of the number and divide it by 3. So if the digits added together equal 8 then the number has a remainder of 2 since 8 divided by 3 has a remainder of 2.

For example, find the remainder on dividing 1,342,568 by 3.

The digit sum of 1342568 is 1+3+4+2+5+6+8 = 29.

Again, the digit sum of 29 = 2+9 = 11 = 2

So, the remainder will be 2.

Another example: Take 34,259,677,858.

The digit sum of the number is 3+4+2+5+9+6+7+7+8+5+8 = 64.

Now, the digit sum of 64 is 6+4 = 10 = 1.

So, the remainder is 1.

Similarly, the digit sum of 54,670,329,845 is 53 i.e. (5+3=) 8.

When we divide 8 by 3, we get remainder 2.

So the answer will be 2.