How many zeros end in the product of all natural numbers from 12 to 40 inclusive?
| May 3, 2021 | education
When multiplying all natural factors from 12 to 40, inclusive, each 0 that is added at the end of the resulting product is obtained by multiplying a pair of numbers, one of which ends in 5, and the other ends in 2, as well as when multiplying by a number that ends in 0.
In this sequence of natural factors, there are 3 pairs of factors in which one number ends in 5, and the other ends in 2: 12 * 15, 22 * 25, 32 * 35, as well as 3 factors that ends in 0: 20, 30, 40.
Therefore, at the end of the product of natural factors from 12 to 40, inclusive, there are 6 zeros.
Answer: this work ends with 6 zeros.
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