Question

The highest power of 100 which divides 100! is

Answer 1

Given. The number is 100!

To find. The highest power 100 which divides 100!

Solution.

Here the number of tailing zeroes in 100! is

= [100 ÷ 5] + [100 ÷ 25], where [] denotes the greatest integer value and we take only first two terms because the other terms, like 125, will give a result less that 1 itself

= 20 + 4

= 24

This shows that there are 24 zeroes in the tail of 100!

i.e., 100! = a valid number × 10²⁴

or, 100! = a valid number × 100¹²

We see that the power of 100 is 12 in 100!'s value.

Answer. Therefore, the highest power of 100 which divides 100! is 12.