Explain why 7 × 11 ×13 +13 and 7 ×6 ×5 ×4 ×3 ×2× 1× 5 are composite numbers?

Sol. We have, 7 x 11 x 13 + 13 = 1001 + 13 = 1014
1014 =2 x 3 x 13 × 13

So, it is the product of more than two prime numbers. 2, 3 and 13.

Hence, it is a composite number. 7 x 6x 5x 4 x 3 x 2 x 1 x 3 x 2 x 1 + 5 = 5040+5=5045
5045 = 5 x 1009

It is the product of prime factors 5 and 1009.

Hence, it is a composite number.