Find the unit digit of 4537^2872Options :1793

The unit digit of any number raised to a power can be found by looking at the cyclicity of the unit digit.

The number 4537 ends in 7. The cyclicity of 7 is 4, which means the unit digit repeats every four powers. The powers of 7 are:

7^1 = 7 7^2 = 49 (ends in 9) 7^3 = 343 (ends in 3) 7^4 = 2401 (ends in 1) 7^5 = 16807 (ends in 7, and the cycle repeats)

Now, we need to find the remainder when 2872 is divided by 4 (the cyclicity of 7) to know which power's unit digit we should look at.

2872 divided by 4 equals 718 with no remainder. This means the unit digit of 4537^2872 is the same as the unit digit of 7^4, which is 1.

So, the unit digit of 4537^2872 is 1.