Question

Сколькими нулями заканчивается произведение всех чисел от 500 до 2017?​

Answer 1

Ответ:

Пошаговое объяснение:

3 нулями

Answer 2

Calculating the Number of Zeroes in the Product of Numbers from 500 to 2017

To calculate the number of zeroes at the end of the product of all numbers from 500 to 2017, we need to find the number of factors of 2 and 5 in the product. The number of trailing zeroes in the product will be equal to the minimum of the number of factors of 2 and 5.

The number of factors of 5 will always be less than the number of factors of 2, so we only need to count the number of factors of 5.

Finding the Number of Factors of 5

To find the number of factors of 5 in the product of all numbers from 500 to 2017, we can use the formula:

Number of factors of 5 = floor(n/5) + floor(n/25) + floor(n/125) + ...

Where n is the upper limit of the range (2017 in this case).

Using this formula, we can calculate the number of factors of 5 in the product of all numbers from 500 to 2017.

Calculation

Using the formula, we can calculate the number of factors of 5 in the product of all numbers from 500 to 2017:

Number of factors of 5 = floor(2017/5) + floor(2017/25) + floor(2017/125) + ...

Number of factors of 5 = 403 + 80 + 16 + 3 = 502

Conclusion

Therefore, the product of all numbers from 500 to 2017 ends with 502 zeroes.

(#1)