Question

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

Answer 1

Given $7\times 11\times 13+13$

$=13\times (7\times 11+1)=3\times 78$

This number is multiple of two integers.Hence it has more than two factors.Hence it is a composite number.

similarly in

$7\times 6$$\times 5$$\times 4$$\times 3$ $\times 2$$\times 1+5$

$=5$($7\times 6$$\times 4$$\times 3$ $\times 2$$\times 1+1)=5\times 1009$

This number is multiple of two integers.Hence it has more than two factors.Hence it is a composite number.