What is the remainder when 2^71 is divided by 15 ?

Question

A. 1
B. 2
C. 4
D. 8
E. 14

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Adit_ · Answer

2^4/15 gives remainder 1.
Therefore 2^68/15 also gives remainder 1.
We need 2^3 more to 2^68 to get to 2^71
Therefore Remainder(2^3/15)=8

Answer:  Option D

Dereno · Answer

Always look for a number which either gives a positive or negative remainder in lowest form.

2^4 =16 is the smallest number.

Thus, 16 when divided by 15 leaves a remainder +1.

2^3 * (2^4)*17 when divided by 15 gives us 8 * (16^17).

Thus, the remainder is  8.

Option D.

poojaarora1818 · Answer

Can we solve this by applying the cyclicity concept?

As we know, the cycle repeats every 2^4.

Cyclicity of 2

2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 6

If we take the lower number, 68, before 71, it is completely divisible by 4, and the remainder is 3(71-68=3). As we know, 2^3 = 8.

So, 2^71, when divisible by 15, would leave the remainder 8.

Answer: Option D

vasu1104 · Answer

cyclicity of 2 is 4. (2,4,8,6)

when raised to power 71, the unit digit will be 8.
when 8 divided by 15, remainder will be 8 itself.

ans D

ExpertsGlobal5 · Answer

Video explanation:    https://www.youtube.com/watch?v=5is-Ce4492A

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