Find the remainder when 3 100 is divided by 7

Asked by admin @ 07/08/2021 in Math viewed by 338 People

Find the remainder of 3^100 when divided by 7.

Answered by admin @ 07/08/2021

Given:

3¹⁰⁰ when divided by 7

To find:

The remainder

Solution:

We will solve this by the remainder theorem,

so, we will write the 3 to the power 100 in terms of the nearest to the multiple of the 7

$\frac{3^{100}}{7}$
$\frac{(3^{3})^{33}.3}{7}$
$\frac{27^{33}.3}{7}$

we can write 27 as 28-1

$\frac{(28-1)^{33}.3}{7}$

28 is the multiple of 7 so we get:

$\frac{(-1)^{33}.3}{7}$
$\frac{-3}{7}$

We have the negative remainder that is -3,

to find the positive remainder we just add 7 to it.

-3+7 = +4

So the remainder is +4

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