To solve this question, recall that:

Prime numbers are whole numbers whose only factors are 1 and the number itself

Composite numbers are positive integers that have factors other than 1 and the themselves.

Now, simplify 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5

On simplifying them, we find that both the numbers have more than two factors. So, if the number has more than two factors, it will be composite

it can be observed that

7 × 11 × 13 + 13 = (7 × 11 + 1)

= (77 + 1)

= 13 ×

= 13 × × 6 × 1

= 13 × 13 × 2 × × 1

The given number has 2, 3, 13, and 1 as its factors. Therefore, it is a composite number.

Now, 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 = × ( 7 × 6 × 4 × 3 × 2 × 1 + 1)

= × (1008 + 1)

= 5 × × 1

1009 cannot be factorized further.Therefore, the given expression has 5,1009 and 1 as its factors. Hence, it is a number.