Explainwhy 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4× 3 × 2 × 1 + 5 are composite numbers.

Numbersare of two types - prime and composite. Prime numbers can be dividedby 1 and only itself, whereas composite numbers have factors otherthan 1 and itself.

It can beobserved that

7 ×11 × 13 + 13 = 13 × (7 × 11 + 1) = 13 × (77 +1)

= 13 × 78

= 13 ×13 × 6

The givenexpression has 6 and 13 as its factors. Therefore, it is a compositenumber.

7 ×6 × 5 × 4 × 3 × 2 × 1 + 5 = 5 ×(7× 6 × 4 × 3 × 2 × 1 + 1)

= 5 × (1008 + 1)

= 5 ×1009

1009cannot be factorised further. Therefore, the given expression has 5and 1009 as its factors. Hence, it is a composite number.