Question

$\frac{155!}{{20}^n}$ is an integer. Find the highest possible value of n for this to be true.

• A. 77
• B. 38
• C. 75
• D. 37

Answer 1

The correct option is B 38

The power of 20 which would divide 155! would be given by the power of 5's which would divide 155! since $20=2^2\times 5$ and the number of 2s in any factorial would always be greater than the number of 5s in the factorial. 31+6+1=38. Option (b) is correct.