Question

сколькими нулями оканчивается значения произведения от 1 до 10, от 1 до 20, от 1 до 30

Answer 1

Количество нулей определяется количеством 5 в произведении.
В числе 10! две 5, одна просто 5, а другая в числе 10 = 2*5. Значит, 2 нуля.
В числе 20! четыре 5, это 5, 10, 15 и 20. Поэтому 4 нуля.
В числе 30! семь 5, это 5, 10, 15, 20, 25 = 5*5, 30. Поэтому 7 нулей.

Answer 2

Произведение от 1 до 10 обычно обозначают 10! (!-факториал) и 10! оканчивается на 2 нуля
20! оканчивается на 4 нуля, а 30! соответственно на 6 нулей

Answer 3

Number of Zeros at the End of the Product

The number of zeros at the end of a product depends on the number of factors that contribute to the product. To determine the number of zeros at the end of a product, we need to count the number of factors that are divisible by 10.

Let's calculate the number of zeros at the end of the product from 1 to 10, 1 to 20, and 1 to 30.

Product from 1 to 10

To calculate the product from 1 to 10, we multiply all the numbers together: 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10.

To determine the number of zeros at the end of this product, we need to count the number of factors that are divisible by 10. In this case, we have two factors that are divisible by 10: 10 and 5. Therefore, the product from 1 to 10 ends with two zeros.

Product from 1 to 20

To calculate the product from 1 to 20, we multiply all the numbers together: 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 * 12 * 13 * 14 * 15 * 16 * 17 * 18 * 19 * 20.

To determine the number of zeros at the end of this product, we need to count the number of factors that are divisible by 10. In this case, we have four factors that are divisible by 10: 10, 20, 15, and 5. Therefore, the product from 1 to 20 ends with four zeros.

Product from 1 to 30

To calculate the product from 1 to 30, we multiply all the numbers together: 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 * 12 * 13 * 14 * 15 * 16 * 17 * 18 * 19 * 20 * 21 * 22 * 23 * 24 * 25 * 26 * 27 * 28 * 29 * 30.

To determine the number of zeros at the end of this product, we need to count the number of factors that are divisible by 10. In this case, we have six factors that are divisible by 10: 10, 20, 30, 15, 25, and 5. Therefore, the product from 1 to 30 ends with six zeros.

Conclusion

The number of zeros at the end of the product from 1 to 10 is 2, from 1 to 20 is 4, and from 1 to 30 is 6.

Please note that the number of zeros at the end of the product increases as the range of numbers being multiplied increases.