Find the number of zeros in 35! ?203558

To find the number of zeros in 35!, we need to find the number of times 10 is a factor in the product. Since 10 = 2 * 5, we need to find the number of times 2 and 5 are factors in the product.

Since 2 is a factor more often than 5 in any given range of numbers, we only need to count the number of times 5 is a factor in the numbers from 1 to 35.

Here's how we do it:

1. Divide 35 by 5. The quotient is 7. This means that there are 7 numbers that are multiples of 5 between 1 and 35.

2. But wait, some numbers may have more than one 5 as a factor. For example, 25 = 5 * 5. So, we need to count these extra 5s as well. To do this, we divide 35 by 25. The quotient is 1. This means that there is 1 number that has at least two 5s as a factor between 1 and 35.

3. Add up the two counts: 7 (from step 1) + 1 (from step 2) = 8.

So, there are 8 zeros at the end of 35!.