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The following division problems all have remainde…

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Problem 67 Easy Difficulty

The following division problems all have remainders.
$$7 1 \div { 1 6 , 6 2 0 }$$

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Video by Kumareshwaran Rathinasabapathy

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Prealgebra

Chapter 1

Whole Numbers

Section 6

Division with Whole Numbers

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Video Transcript

Here we find the remainder when six raised to the power of 11 -6 is divided by 11. So for this will be replacing this concept that is F. P. is a prime number. Then a raise to the power of P is congruent to a more p. So first we'll find the reminder when 6 11 is Divided by 11 using this concept. So I'm going to I don't ask like this one. So this is uh six, His to the power of 11. Congruent to six more 11. As you can see here this 11 is the P. And uh Which is in fact is a prime number. 11 is a prime number. So that's why we can replace this concept and therefore this six is represented by a. So this completely matches with this concept which means we can say that the sixes the remainder when 6411 is divided by 11. Uh No According to the basic concept of modular arithmetic, this is equal to six power 11 minus six Is equal to 11 times soft cape parquet, some number which means this is being divisible by 11. Uh if it is reducible by lovin, then the remainder that is obtained is zero. So therefore the reminder When 6 11 -6 is started by 11 0. So this is the answer for this question.

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Charles P. McKeague

Prealgebra

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