Question

Last digit (unit digit) of 2^2014

Answer 1

4

Explanation:

Let's find a pattern.

2^0=1

2^1=2

2^2=4

2^3=8

2^4=16

2^5=32

2^6=64

2^7=128

2^8=256

So starting after power of 0, the pattern begins at power=1. The pattern is 2,4,8,6 for the units digit. Since the pattern repeats in 4, then we shall divide the power in question by 4 seeking it's remainder.

Remainder=1 implies unit digit is 2 (see 2^1=2)

Remainder=2 implies unit digit is 4 (see 2^2=4)

Remainder=3 implies unit digit is 8 (see 2^3=8)

Remainder=0 implies unit digit is 6 (see 2^4=16)

2014/4 = 503 + 2/4

So remainder=2 implies unit digit is 4.