Is the multiplication

$$
79133 \times 111107=8792240231
$$

exact? (Without a calculator)
The answer is NO. We use two results:

Let $n$ be an integer. The remainder of the division of $n$ by 9 is equal to the remainder of the division by 9 of the sum of the digits of $n$.

Let $a, b$ be integers. The remainder of the division of $a \times b$ by 9 is equal to the remainder of the division by 9 of the product of the remainders of the divisions of $a$ and $b$ by 9.