Question

Сколькими нулями оканчивается произведение чисел от 1 до 30 включительно

Answer 1

С 1 нулём  так  понятно

Answer 2

Произведение чисел от 1 до 30 включительно оканчивается на 6 нулей.

To arrive at this answer, we can calculate the factorial of 30, which is the product of all the numbers from 1 to 30. The factorial of a number n is denoted by n! and is calculated by multiplying all the numbers from 1 to n.

The factorial of 30 can be calculated as follows: 1! * 2! * 3! * ... * 30!

However, instead of calculating the entire factorial, we can focus on the number of trailing zeros in the factorial. The number of trailing zeros in a factorial is determined by the number of factors of 10 in the product. Since 10 is the product of 2 and 5, we need to count the number of pairs of 2 and 5 in the product.

In the range from 1 to 30, there are more factors of 2 than factors of 5. Therefore, we only need to count the number of factors of 5.

Let's calculate the number of factors of 5 in the range from 1 to 30:

- 5: 1 factor of 5 - 10: 1 factor of 5 - 15: 1 factor of 5 - 20: 1 factor of 5 - 25: 2 factors of 5 - 30: 1 factor of 5

Adding up the factors of 5, we get a total of 6 factors of 5 in the range from 1 to 30. Therefore, the product of the numbers from 1 to 30 ends with 6 zeros.

Please note that this calculation is based on the concept of counting factors of 5, and it is not necessary to calculate the entire factorial to determine the number of trailing zeros.