Question

Explain why $7\times 11\times 13+13$ and $7\times 6\times 5\times 4\times 3\times 2\times 1+5$ are composite numbers.

Answer 1

$7\times 11\times 13+13$
Taking 13 common, we get
$7\times 11\times 13+13=13(7\times 11+1)$
13(77 + 1 )
13 (78)
It is a product of two numbers, both greater than 1. Hence, it is a composite number.

$7\times 6\times 5\times 4\times 3\times 2\times 1+5$
Taking 5 common, we get
$7\times 6\times 5\times 4\times 3\times 2\times 1+5=5(7\times 6\times 4\times 3\times 2\times 1+1)$
5(1008 + 1)
5(1009)
It is a product of two numbers, both greater than 1. So, it is a composite number.