Question

What is the highest power of 5 contained in 40!?

Answer 1

Answer:

Please see the attachment

Answer 2

Answer:

The highest power of $5$ contained in $40!$ is $9$.

Step-by-step explanation:

We know,

$40 !=2^{a} \cdot 3^{b} \cdot 5 \cdot 7^{c} \ldots .$

The number of $5^{-1}$ in $40 !$ is,

$\frac{40}{5} +\frac{40}{5^2}=8+1$

$=9$

Therefore,

The highest power of $5$ contained in $40!$ is $9$.