Answer:
To find the number of terminal (trailing) zeros in 30!, you can count the number of times 10 is a factor in the expansion of 30!. Since 10 is the product of 2 and 5, you need to count the number of pairs of 2 and 5 in the prime factorization of the numbers from 1 to 30.
There are more 2s than 5s among the prime factors of those numbers, so you need to count the number of 5s. To do this, divide 30 by 5, which gives you 6. However, there are also multiples of 25 (5^2) that contribute an additional factor of 5. There is one multiple of 25 in the range of 1 to 30 (which is 25 itself).
So, you have 6 + 1 = 7 factors of 5 in the prime factorization of 30!. Therefore, 30! has 7 terminal zeros.