Question

Find remainder when 7^805
divided by 24​

Answer 1

Answer: 1

Step-by-step explanation:

7^2 = 1 mod 24

(7^2)^500 = (1)^500 mod 24

7^1000 = 1 mod 24

so answer is 1.

here we use application of division algorithm that is Modular arithmetic.

when a = q n +r ,where q is remainder upon dividing a by n , we write a mod n = r or a = r mod n.

more generally , if a and b are integers and n is a positive integer , we often write a= b mod n whenever n divides a - b

Answer 2

Hello Buddy,

Thanks For Asking the Question :)

Your Answer is Below

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Question :-

$\mathrm{Find\:the\:Remainder\:when\:7^{805}\:divided\:by\:24 }\quad$

Explanation :-

⇒ $7^{805}= (7^{4})^{201} \times 7$

⇒ $(2401)^{201} \times 7$

• $\mathrm {When\:(2401)^{201}\:is\:divided\:by\:24,\:the\; remainder\:is\:1 \ [ \because 2401=24\times100+1]}$

⇒ 1 × 7

⇒ 7

            ${\large{\boxed{\mathrm{\therefore\:Remainder\:when\:7^{805}\:is\:divided\:by\:24\:is\:7 }}}}$

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Hope It Helps You Dear ! :D      ^_^

By Abhiram5566

                                  MARK ME AS BRAINLIEST ANSWER

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