Find the no of zero’s in 124!. Options : 20 24 28 32

The number of zeros at the end of a factorial can be found by calculating the number of pairs of 2 and 5 in the prime factorization of the number. Since there are always more 2s than 5s, we only need to count the number of 5s.

Here are the steps to find the number of zeros in 124!:

1. Divide 124 by 5, you get 24.8. Since we cannot have a fraction of a factor, we take the integer part, which is 24. This is the number of numbers less than or equal to 124 that are divisible by 5.

2. Divide 124 by 25 (5^2), you get 4.96. Again, we take the integer part, which is 4. This is the number of numbers less than or equal to 124 that are divisible by 25 (or 5 twice).

3. Divide 124 by 125 (5^3), you get 0.992. The integer part is 0. This is the number of numbers less than or equal to 124 that are divisible by 125 (or 5 three times).

4. Add up these counts: 24 + 4 + 0 = 28.

So, the number of zeros at the end of 124! is 28. Therefore, the correct option is 28.