Is the multiplication:

$$
79133 \times 111107=8794230231
$$

exact? (Without a calculator)
Let's observe the equality modulo 3.

$-79133 \equiv 7+9+1+3+3 \equiv 2(\bmod 3)$

$-111107 \equiv 1+1+1+1+0+7 \equiv 2(\bmod 3)$

$-8794230231 \equiv 8+7+9+4+2+3+0+2+3+1 \equiv 0(\bmod 3)$[^1]

Now, $2 \times 2 \equiv 1 \not \equiv 0(\bmod 3)($ the product of numbers not multiples of 3 is not a multiple of 3$)$, so the multiplication is incorrect. (correct result: 8792230231 )