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Given: Numbers 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5

To show: Why the numbers are composite

Explanation:

Numbers are of two types - prime and composite.

Prime numbers have only two factors namely 1 and the number itself whereas composite numbers have factors other than 1 and itself.

It can be observed that

7 × 11 × 13 + 13 = 13 × (7 × 11 + 1)

= 13 × (77 + 1)

= 13 × 78

= 13 × 13 × 6

The given expression has 6 and 13 as its factors. Therefore, it is a composite number.

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

= 5 × (1008 + 1)

= 5 ×1009

In the above we observe that 1009 cannot be factorized further. Therefore, the given expression has 5 and 1009 as its factors. Hence, it is a composite number.