How many zeros are there in 100! ?

To find the number of zeros in 100!, we need to determine how many times 100! is divisible by 10. Since 10 is the product of 2 and 5, the number of zeros in 100! depends on how many times 100! contains the factor 5. There will always be more factors of 2 than factors of 5, so the number of zeros is determined by the number of factors of 5.

To calculate this, we use the following process:

Divide 100 by 5:
100 ÷ 5 = 20.
This means there are 20 multiples of 5 up to 100.

Divide 100 by 25 (5^2):
100 ÷ 25 = 4.
This means there are 4 multiples of 25 up to 100, each of which contributes an additional factor of 5.

Divide 100 by 125 (5^3):
100 ÷ 125 = 0.
Since 100 is less than 125, there are no multiples of 125 up to 100.

Now, sum the results: 20 (from multiples of 5) + 4 (from multiples of 25) = 24.

Thus, the number of zeros in 100! is 24.