Question

Find the highest power of 25 in 100!___

Answer 1

$25=5^2$
In this case, we will first find out the exponents of 5 and then divide it by 2(actually the power) to find out the exponents of 25.
$\frac{100}{5^x}=\left[\frac{100}{5}\right]+\left[\frac{100}{5^2}\right]=20+4=24$
So $\frac{100}{{25}^x}=\frac{24}{2}=12$