Question

The remainder when $(3{)}^{67!}$ is divided by 80:

• A. 1
• B. 2
• C. can't be determined

Answer 1

The correct option is A 1

$3^4=81so\frac{3^{4n}}{80}$ gives remainder 1.
Thus $\frac{3^{67!}}{80}$ will also give the remainder 1.
Since 67! = 4n for a positive integer n.