4.35. How many zeros does the product of all integers from 1 to 100 inclusive end with?
4.35. Answer: 24. Among the numbers from 1 to 100, there are 20 numbers divisible by 5, and among the numbers divisible by 5, there are 4 numbers divisible by 25 (there are no numbers divisible by 125 among the given numbers). Therefore, the considered product is divisible by $5^{24}$ and not divisible by $5^{25}$. It is also clear that it is divisible by $2^{24}$.