Question

Делится ли число a=3*5*5*7*7*11 на 245 без остатка? Объясните ответ.

Answer 1

Ответ:

делится т.к. закнчивается на 5

Answer 2

Ответ:да

Пошаговое объяснение:

КОРОЧЕ, 3•5•7•7•5•11=40425

мы умножаем любое число на 40425 и получаем число, которое делится на 245 т.к. один множитель(тоесть 40425) делится на 245 без остатка

Answer 3

To determine whether the number $a = 3 \times 5 \times 5 \times 7 \times 7 \times 11$ is divisible by 245 without a remainder, we need to check if 245 is a divisor of $a$ (i.e., $a$ is divisible by 245).

The prime factorization of 245 is $245 = 5 \times 7 \times 7$. To check if $a$ is divisible by 245, we need to check if it contains all the prime factors of 245 and in sufficient quantity.

Let's analyze the prime factorization of $a$: $a = 3 \times 5 \times 5 \times 7 \times 7 \times 11$.

From this factorization, we can see that $a$ contains all the prime factors of 245 ($5$, $7$, and $7$) in sufficient quantity, as each factor in 245 appears at least once in the factorization of $a$.

Therefore, $a$ is divisible by 245 without a remainder, because it contains all the prime factors of 245 with sufficient multiplicity. In other words, $a$ can be expressed as $245 \times n$ for some integer $n$.