Math, asked by sunina, 1 year ago

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

Answers

Answered by DevendraLal
38

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

Answered by Hunar195
2

Answer:

4

Step-by-step explanation:

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