Question

Explain why $7\ast 11\ast 13+13$ and $7\ast 6\ast 5\ast 4\ast 3\ast 2\ast 1+5$ are composite number.

Answer 1

The numbers are prime numbers and composite numbers.
A prime number can be divided by $1$ and itself.
A composite number has a factor other than $1$ and itself.
$7\ast 11\ast 13+13=13(7\ast 11\ast 1+1)=1=13\ast 78$
$=13\ast 13\ast 6=13\ast 13\ast 2\ast 3$
The given expression has $2,3$ and $13$ as its factors.
$\therefore$ It is a composite number.
$7\ast 6\ast 5\ast 4\ast 3\ast 2\ast 1+5$
$=5(7\ast 6\ast 4\ast 3\ast 2\ast 1+1)$
$=5(1008+1)=5\ast 1009$.
The given expression has $5$ and $1009$ as its factors.
$\therefore$ It is a composite number.