Explain Why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 Are Composite Numbers

Video Explanation

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

7 × 11 × 13 + 13

= 13 (7 × 11 + 1)

= 13 (77 + 1)

= 13 × 78

Since the number can be written as a product of two integers greater than 1, it is a composite number.

7 × 6 × 5 × 4 × 3 × 2 × 1 + 5

= 7! + 5

= 5 (7 × 6 × 4 × 3 × 2 × 1 + 1)

= 5 (1008 + 1)

= 5 × 1009

Since this number can also be expressed as a product of two integers greater than 1, it is a composite number.

Both given numbers can be expressed as a product of integers greater than 1. Therefore,

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

Thus, by factorising the given expressions, we conclude that both numbers are composite because they have factors other than 1 and themselves.

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