How many number of zeros in 100!

To find the number of zeros in 100 factorial, we need to find the number of times 10 is a factor in the numbers from 1 to 100.

10 is a product of 2 and 5. In the numbers from 1 to 100, there are more numbers that are multiples of 2 than 5. So, we just need to count the number of times 5 is a factor.

Here's how to do it:

1. Divide 100 by 5. This gives 20. This means there are 20 numbers that are multiples of 5 between 1 and 100.

2. However, some numbers like 25, 50, 75, and 100 are multiples of 5 twice. So, we need to count these again. We do this by dividing 100 by 25 (5^2). This gives 4.

3. There is also one number (100) which is a multiple of 5 three times. We find this by dividing 100 by 125 (5^3), but since 125 > 100, we don't consider this.

4. Add up the numbers from steps 1 and 2. This gives 20 + 4 = 24.

So, there are 24 zeros at the end of 100 factorial.