Find the reminder of the division

(8^33) : 6

The remainder is 2.

Step-by-step explanation:

Use modular arithmetic.

If the remainder is x then 8^33 mod 6 = x.

8^3 = 512 = 2 mod 6

8^6 = (8^3 * 8^3) mod 6 = (2*2) mod 6 = 4 mod 6

8^30 mod 6 = (8^6) ^5 mod 6 = 4^5 mod 6 = 1024 mod 6

= 4 mod 6.

Finally 8^33 mod 6 = (8^3 * 8^30) mod 6 = (2 * 4) mod 6

= 8 mod 6 = 2.