Question

Explain why $7\times 11\times 13+13$ and $7\times 6\times 5\times 4\times 3\times 2\times 1+5$ are composite numbers

Answer 1

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,$7\times 11\times 13+13$

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

$=13\times (77+1)$

$=13\times 78$

$=13\times 13\times 6$

$=13\times 13\times 3\times 2$

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

It is a composite number.

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

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

$=5(1008+1)$

$=5\left(1009\right)$
Now, Hence, it has more then two factors $(5\times 1009)$ and $(1,5,1009)$
It is also a composite number.