Find the number of trailing zeroes in 155!

Sure, to find the number of trailing zeroes in 155!, we need to find the number of factors of 10 in the factorial. A factor of 10 is made from multiplying 2 and 5. In a factorial, there are always more factors of 2 than 5. So, we just need to count the number of factors of 5.

Here are the steps:

1. Divide 155 by 5. The result is 31 (ignoring the remainder). This is the number of numbers less than or equal to 155 that are divisible by 5.

2. However, numbers like 25, 50, 75, 100, 125, 150 contribute more than one factor of 5. To account for this, divide 155 by 25. The result is 6.

3. Numbers like 125 contribute more than two factors of 5. To account for this, divide 155 by 125. The result is 1.

4. Add up all these counts: 31 + 6 + 1 = 38.

So, 155! has 38 trailing zeroes.