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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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Solution

A number is said to be composite number, if it has more than two factors, So lets check the number of factors for given numbers.
Since,7×11×13+13

=13(7×11+1)

=13×(77+1)

=13×78

=13×13×6

=13×13×3×2

Hence, it has more then two factors (13×78) and (1,2,3,13,)

It is a composite number.

7×6×5×4×3×2×1+5

=5((7×6×4×3×2×1)+1)

=5(1008+1)

=5(1009)
Now, Hence, it has more then two factors (5×1009) and (1,5,1009)
It is also a composite number.


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