PROBLEM 1-9-2

What is the last digit of 2^31921?

(^ means to the power of...)

SOLUTION 1-9-2

2^1 = 2

2^2 = 4

2^3 = 8

2^4 = 16

2^5 = 32

2^6 = 64

2^7 = 128

2^8 = 256

2^9 = 512

2^10 = 1024

2^11 = 2048

2^12 = 4096

 

Looking at the pattern, any odd power ends in 2 or 8.

31921 / 4 = 7980.25 or 7980 and 1/4

1/4 is the group of 4 (looking at the last digit: 2,4,8,6); therefore, the last digit is a 2.