How many trailing zeros will be there in 2302! (factorial of 2302)?

The number of trailing zeros in a factorial can be found by calculating the number of pairs of 2 and 5 in its prime factors, since 10 = 2 * 5. However, since factorials have far more 2s than 5s, we only need to count the number of 5s.

Here are the steps to find the number of trailing zeros in 2302!:

1. Divide 2302 by 5. The quotient is 460. This is the number of numbers less than or equal to 2302 that have 5 as a factor.

2. Divide 2302 by 25 (5^2). The quotient is 92. This is the number of numbers less than or equal to 2302 that have 25 as a factor.

3. Divide 2302 by 125 (5^3). The quotient is 18. This is the number of numbers less than or equal to 2302 that have 125 as a factor.

4. Divide 2302 by 625 (5^4). The quotient is 3. This is the number of numbers less than or equal to 2302 that have 625 as a factor.

5. Add up all these quotients: 460 + 92 + 18 + 3 = 573.

So, 2302! has 573 trailing zeros.