Question

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

Answer 1

Composite numbers are numbers that have more than two factors.

Example: $9$ is a composite number as it has $3$ factors i.e $1,3$ and $9.$

$1$ is the factor of every number.

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

Taking $13$ common, we get

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

$=13(77+1)$

$=13\times 78$

It has two factors $13$ and $78,$ other than $1.$ Hence, it is a composite number.

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

Taking $5$ common, we get

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

$=5(1008+1)$

$=5\left(1009\right)$

It has two factors $5$ and $1009,$ other than $1.$ So, it is a composite number.