Question

Explain why $(17\times 5\times 11\times 3\times 2+2\times 11)$ is a composite number?

Answer 1

$17\times 5\times 11\times 3\times 2+2\times 11=17\times 5\times 3\times 22+22$

$=22(17\times 5\times 3+1)$
$=22(255+1)=2\times 11\times 256$ -----(i)


Equation (i) is divisible by 2, 11 and 256, so it has more than 2 prime factors.

$\therefore (17\times 5\times 11\times 3\times 2+2\times 11)$ is a composite number.