hsab hsab
  • 15-07-2016
  • Mathematics
contestada

What is the unit's digit of 3127 to the power of 173

Respuesta :

Csxl Csxl
  • 16-07-2016
3127^173 ≡ 7^173 mod 10

Now - let's look at the powers of 7 mod 10:

7^1 = 7 mod 10
7^2 = 49 ≡ 9 mod 10
7^3 ≡ 3 mod 10
7^4 ≡ 1 mod 10

And this cycle repeats. So

7^173 ≡ 7^1 ≡ 7 mod 10

The last digit is 7.
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