What Is The Remainder When 4^96 Is Divided By 6 GMAT Problem Solving

Remainder when \(4^1\)is divided by 6 = 4

Remainder when \(4^2\) (=16) is divided by 6 = 4

Remainder when \(4^3\)  (=64) is divided by 6 = 4

Thus, any power of 4 when divided by 6 leaves a remainder of 4.

Correct option: E

If we take \(4^1\) divided by 6, the remainder is 4

\(4^2\) divided by 6, remainder is 4

\(4^3\) divided by 6, remainder is 0

\(4^4 \)divided by 6, remainder is 4
And so on
So, when 4 has even a number of powers, it will always give remainder 4 on dividing by 6

The remainder of \(4^{96}\) /6 is 4 

Correct option: E

Solve it using the cyclicity rule which for 4 is : 4,6, …

So, at  \(4^{96}\) we would get units digits ending with 6

Upon checking for any even power raised to 4 i.e \(4^{even power}\) and divided by 6, we always get remainder as 4 eg \(4^2\), \(4^4\) .... so \(4^{96}\) will also give remainder as 4

Correct option: E