Question

find the remainder of 3 raised to power 2017 is divided by 10​

Answer 1

Answer:

3

Step-by-step explanation:

Working modulo 10, we have

3² = 9 ≡ -1 (mod 10)

so

   3²⁰¹⁷ = 3 × 3²⁰¹⁶ = 3 × (3²)¹⁰⁰⁸ ≡ 3 × (-1)¹⁰⁰⁸ = 3 × 1 = 3 (mod 10)

If you're not comfortable with modular arithmetic, you can instead note that 3⁴ = 81, which ends in 1.  So

 3²⁰¹⁷ = 3 × 3²⁰¹⁶ = 3 × (3⁴)⁵⁰⁴ = 3 × 81 × 81 × 81 × ... × 81

so the final digit will be 3.

Hope this helps you!