Find the number of zeros at the end of the 120! + 230! + 40! + 450! + 60! + 670!

To find the number of zeros at the end of the sum of factorials, we need to find the factorial with the least number of zeros, because the number of zeros at the end of a factorial is determined by the number of pairs of 2 and 5 in its prime factors, and the number of 5s is always less than the number of 2s.

Here are the steps:

1. Find the factorial with the least number of zeros. In this case, it's 40!.
2. Calculate the number of zeros at the end of 40!. The number of zeros is determined by the number of 5s in the prime factors of 40!. Since 40/5 = 8, there are 8 zeros at the end of 40!.
3. Therefore, the number of zeros at the end of the sum of the factorials is 8.