What is the remainder when 7^381 is divided by 5 ?

Question

A) 0
B) 1
C) 2
D) 3
E) 4

yangsta8 · Answer

7^0 = 1
7^1 = 7
7^2 = 49
7^3 = 343
7^4 = .....1
7^5 = .....7
And so on...

381/4 = 95 r 1 so the last number is a 7.
so when 7^381 is divided by 5 the remainder is 2, ANS = C

verbalfight · Answer

C it is

pattern of remainders

(7^1)/5 rem=2
(7^2)/5 rem=4
(7^3)/5 rem=3
(7^4)/5 rem=1
(7^5)/5 rem=2 again..pattern repeats by cycle of 4

now, 381/4 rem =1. (here 4 is the cyclicity)
=> 1st remainder in the pattern. which is 2

Syed · Answer

I also agree that the remainder is '2' (using the last digit of the powers of 7). Could we have the official answer please?

jeeteshsingh · Answer

(7^381) Mod 5
= (7 Mod 5)^381
= (2) ^ 381
= (2 Mod 5)^381
= (2 Mod 5)^380 * (2 Mod 5)
= (4 Mod 5)^190 * 2
= (-1)^190 * 2
= 2

Therefore B...!

Bullet · Answer

7 has cyclicity of 4, 381 mod 4 and the remainder 1. So 7^1 and 7^381 has the same last digit.

7 Mod 5 leads to 2 as remainder.

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