Question

Find the remainder of 9876^4 when it is divided by 7

Answer 1

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Answer 2

Answer:

The remainder is 1.

Step-by-step explanation:

We need to find the 9876^4 when it is divided by 7. It means, we have to find the value of

$9876^4\text{(mod 7)}$

It can be written as

$9876\times 9876\times 9876\times 9876\text{(mod 7)}$

Using the property of modulo, we get

$9876\text{(mod 7)}\times 9876\text{(mod 7)}\times 9876\text{(mod 7)}\times 9876\text{(mod 7)}$

When 9876 is divided by 7, then the remainder is 6.

$6\times 6\times 6\times 6$

$36\times 36$

Now again take mod 7.

$36\text{(mod 7)}\times 36\text{(mod 7)}$

$1\times 1$

$1$

Therefore, the remainder is 1.