Question

Using modular arithmetic,find the remainder when 7^12 is divided by 47

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Answer 1

Answer:Straight answer 17

I know a easy method to do this, let's get started.

Suppose there is a number A and B . And we have to find the remainder when A is divided by B.

And A can be represented as a product of following numbers a,b,c,d etc

A= a*b*c*d*…

Remainder of A when divided by B would be same as dividing a ,b ,c ,d… by B and multiplying their remainder together .

If the number is still big and remainder is difficult to find you can repeat the process.

Answer would be the same

Example for illustration when 88 dvided by 3

88=8*11

Then we will find the remainder of 8 and 11 divided by 3 independently

8%3= 2

11%3= 2

Then we will multiply 2 and 2

Then we will again perform the division of 4 by 3 and remainder would be 1 which is same as the remainder we will get when 88 is decided by 3.

This is a very helpful and easy method to calculate remainder

We can represent 7^12 as( 7^2)^6 or as 49^6.

Then we have to decide 49 by 47 and find it's remainder which will be 2 . After dividing 49 sex times by 47 we will have six 2 . Then we will multiply 2 sex time to get 2^6 which will result in 64 . And at last we will decide 64 by 47 and remainder will be 17.

Step-by-step explanation: