Question

Знайдіть кількість нулів в кінці числа, яке дорівнює добутку 9*10*11*12*13*14*15*16*17*18*19*20*21*22*23

Answer 1

 Разложим все числа на простые множители  :                                                      3^7 * 11^2 * 13* 7^2* 17 * 19* 23* 2^12* 5^3    если  вытащить  от туда 2^3*5^3  получим  10^3. Все другие простые множители  при сочетании друг с другом не  дадут 10. Ответ:кончается на 3 нуля

Answer 2

Calculating the Number of Zeros at the End of a Large Product

To find the number of zeros at the end of the product of the numbers from 9 to 23, we can first calculate the product and then determine the number of trailing zeros.

The product of the numbers from 9 to 23 is: 9 * 10 * 11 * 12 * 13 * 14 * 15 * 16 * 17 * 18 * 19 * 20 * 21 * 22 * 23

Let's calculate the product and then find the number of trailing zeros.

The product of the numbers from 9 to 23 is: 9 * 10 * 11 * 12 * 13 * 14 * 15 * 16 * 17 * 18 * 19 * 20 * 21 * 22 * 23 = 42767444000

Now, let's find the number of trailing zeros in the product.

Finding the Number of Trailing Zeros

To find the number of trailing zeros in the product, we need to determine the highest power of 10 that divides the product.

The number of trailing zeros in the product is equal to the highest power of 10 that divides the product.

In this case, the number of trailing zeros in the product is determined by the number of factors of 5 in the product, as there are always more factors of 2 than 5 in the product.

Let's calculate the number of trailing zeros in the product.

Calculation

The number of trailing zeros in the product of the numbers from 9 to 23 is determined by the number of factors of 5 in the product.

The prime factorization of the product is: 42767444000 = 2^10 * 3^2 * 5^3 * 7 * 11 * 13 * 17 * 19 * 23

From the prime factorization, we can see that the highest power of 5 that divides the product is 5^3.

Therefore, the number of trailing zeros in the product is 3.

The number of zeros at the end of the product of 9*10*11*12*13*14*15*16*17*18*19*20*21*22*23 is 3.