Question

What is the largest power of $20$ contained in $100$ factorial?

Answer 1

Find the largest power of $20$ contained in $100$ factorial.

$20=5\times 2\times 2$

The highest prime factor $20$ is 5.

So, number of power of $20$ will only depend on power of $5$.

Also, $\frac{100}{5}=20,\frac{100}{25}=4$.

Therefore, the power of $5$ is $20+4=24$

Hence, the largest power of $20$ contained in $100$ factorial is $24$.