Q. Find the remainder when 5^297 is divided by 7
Answers
Answered by
3
Step-by-step explanation:
Attachments:
Answered by
5
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
________________________
→ 5^7 = 78125 & Remainder = 5
→ 5^8 = 390625 & Remainder = 4
→ 5^9 = 1953125 & Remainder = 6
→ 5^10 = 9765625 & Remainder = 2.
___________________
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.
Similar questions