#### Question

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

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#### Solution

We have,

7 x 11 x 13 + 13 = 1001 + 13 = 1014

1014 = 2 x 3 x 13 x 13

⇒ it is the product of prime factors

2 x 3 x 13 x 13

Hence it is a composite number

7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 = 2520 + 5 = 2525 and 2525 = 5 x 5 x 101

It is the product of prime factors 5 x 5 x 101

Hence it is a composite number.

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#### Reference Material

Solution for question: Explain Why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 Are Composite Numbers. concept: Fundamental Theorem of Arithmetic. For the course CBSE