Explanation:

To find the number of trailing zeroes in the factorial of 100 (100!), you need to count the number of times 10 is a factor in the product. A factor of 10 is made up of 2 and 5, and there are always more 2s than 5s in factorial products, so you only need to count the 5s.

- Count how many multiples of 5 there are from 1 to 100: 100/5 = 20.

- Count the multiples of 25 (which have an extra 5): 100/25 = 4.

- Count the multiples of 125 (which have yet another extra 5), but it doesn't matter here because 125 > 100.

So, the total is 20 + 4 = 24. Hence, option 3: 24 is correct.

Answer: Option 3: 24