Answer:
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.
