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

Ans: Let’s take both numbers one by one and analyse:

(i) 7 × 11 × 13 + 13

= 13 (7 x 11 + 1)

= 13 x 78

= 13 x 13 x 2 x 3

Since the given number has more than two factors, it is a composite number.

(ii) 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5

= 5 ( 7 × 6 × 4 × 3 × 2  + 1)

= 5 (1009)

= 5 x 1009 x 1

Since the given number has more than two factors, it is also a composite number.

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