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

Answer:

Composite numbers are factors other than 1 and itself.
From here we can observe that :

(a) 7 × 11 × 13 + 13 = 13 (7 × 11 × 1 + 1) = 13 (77 + 1)
= 13 × 78
= 13 × 13 × 6

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

(b) 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 = 5 (7 × 6 × 1 × 4 × 3 × 2 × 1 + 1)
= 5 × (1008 + 1)
= 5 × 1009

1009 can not be factored further. Therefore, this expression has 5 and 1009 as its factors.
Hence, it is a composite number.

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

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

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