How many 0's are at the end of 100! ?

Can someone check if this is correct? Thanks.

My reasoning: numbers that produce 0's at the end are 2, 5 and any other integers 2^r < 100 , 5^s < 100

2^1 = 2

2^2 = 4

2^3 = 8

2^4 = 16

2^5 = 32

2^6 = 64

5^1 = 5

5^2 = 25

r + s = 1 + 2 + 3 + 4 + 5 + 6 + 1 + 2 = 24

There are 24 0's at the end of 100!