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

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Solution:
7 x 13 x 11 + 11 = (7 x 13 + 1) x 11
= (91 + 1) x 11 = 92 x 11
= (2 x 2 x 23) x 11
= 2 x 2 x 11 x 23
Since 7 x 13 x 11 + 11 can be expressed as a product of primes, it is a composite number.
(7 x 6 x 5 x 4 x 3 x 2 x 1) + 3
= (7 x 6 x 5 x 4 x 2 x 1 + 1) x 3
= (1680 + 1) x 3 = 1681 x 3
= (41 x 41) x 3 = 3 x 41 x 41
Since (7 x 6 x 5 x 4 x 3 x 2 x 1) + 3 can be expressed as a product of primes, it is a composite number.

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