Question

Сколько нулей на конце имеет произведение круглых чисел до 100 включительно? Помогите, пожалуйста!

Answer 1

10*20*...*100
Всего 10"круглых чисел-это 10 нулей,но числе 100 два нуля и произведение 2*5 дает еще ноль.Итого 12 нулей.

Answer 2

Number of Zeros at the End of the Product of Numbers up to 100

To determine the number of zeros at the end of the product of numbers up to 100, we need to count the number of factors of 5 in the product. This is because a zero at the end of a number is created by multiplying 10, which is 2 * 5. Since there are more factors of 2 than 5 in the product of numbers up to 100, we only need to count the factors of 5.

To find the number of factors of 5 in the product of numbers up to 100, we can divide each number by 5 and count the number of times the division is exact. However, we also need to consider numbers that have multiple factors of 5, such as 25, 50, and 75. For these numbers, we need to divide them by 5 multiple times.

Let's calculate the number of zeros at the end of the product of numbers up to 100:

1. Divide each number up to 100 by 5 and count the number of times the division is exact. - For numbers from 1 to 100, there are 20 numbers that are divisible by 5. - This gives us 20 factors of 5.

2. Divide each number up to 100 by 25 and count the number of times the division is exact. - For numbers from 1 to 100, there is 1 number (25) that is divisible by 25. - This gives us an additional factor of 5.

Therefore, the total number of factors of 5 in the product of numbers up to 100 is 20 + 1 = 21. This means that the product of numbers up to 100 has 21 zeros at the end.

Answer: The product of numbers up to 100 has 21 zeros at the end.