Question

Q. Find the remainder when 5^297 is divided by 7...with explanation plss​

Answer 1

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Answer 2

Question :-

Find the remainder when 5^297 is divided by 7 ?

Solution :-

Cycle For 7 :-

→ 5^1 = 5 & Remainder = 5 when divided by 7.

→ 5^2 = 25 & Remainder = 4 when divided by 7.

→ 5^3 = 125 & Remainder = 6

→ 5^4 = 625 & Remainder = 2

→ 5^5 = 3125 & Remainder = 3

→ 5^6 = 15625 & Remainder = 1

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→ 5^7 = 78125 & Remainder = 5

→ 5^8 = 390625 & Remainder = 4

→ 5^9 = 1953125 & Remainder = 6

→ 5^10 = 9765625 & Remainder = 2.

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Hence, we Can conclude That, 5, 4, 6, 2, 3, 1, are repeating Remainder.

So,

→ 5^(297)

→ 5^(6*49 + 3)

So, when 297 is divided by 6 it gives Remainder 3.

And, 3rd in The cycle is 6.

Hence, we can say That, when we divide 5^(297) by 7 we will get 6 as a remainder.