Solution:
By the definition of a composite number, we know that if a number is composite, then it means it has factors other than 1 and itself. Therefore, for the given expression;
7 × 11 × 13 + 13
Taking 13 as a common factor, we get,
= 13(7 × 11 × 1 + 1)
= 13(77 + 1)
= 13 × 78
= 13 × 3 × 2 × 13
Hence, 7 × 11 × 13 + 13 is a composite number.
Now let’s take the other number.
7 × 6 × 5 × 4 × 3 × 2 × 1 + 5
Taking 5 as a common factor, we get,
= 5(7 × 6 × 4 × 3 × 2 × 1 + 1)
= 5(1008 + 1)
= 5 × 1009
Hence, 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 is a composite number.