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.

Solution :

We have,  \(7 \times 11 \times 13\) + 13 = 1001 + 13 =1014

1014 = \(2 \times 3 \times 13 \times 13\)

So, it is the product of more than two prime numbers.

2, 3 and 13.

Hence, it is a composite number.

\(7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\) + 5 = 5040 + 5 = 5045

\(\implies\)  5045 = 5 \(\times\) 1009

It is the product of prime factors 5 and 1009.

Hence, it is a composite number.