# How many zeros does the product of all natural numbers from 18 to 45, inclusive, end in?

July 26, 2021 | education

| We get zero if we multiply 5 by an even number. In the range from 18 to 45 inclusive, there are 6 numbers (20,25,30,35,40,45) that are divisible by 5 without a remainder. And plus another number 25 divided by 5 twice: 25: 5 = 5: 5 = 1. That is, it turns out 6 fives and plus one more five, which is obtained by dividing 25 by 5.

It turns out 6 + 1 = 7 fives. There are much more even numbers in the range from 18 to 45, so the product of all natural numbers from 18 to 45 ends with 7 zeros.

Answer: 7 zeros.

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