Question

Explain why 7 × 11 × 13 + 13 is a composite number.

Answer 1

Consider,

7 x 11 x l3 + 13

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

= 13 $\times$ (77+1)

=13 $\times$ 78

$\Rightarrow$ 7 $\times$11 $\times$13 + 13 = 2 $\times$ 3$\times$13 $\times$13

By fundamental theorem of Arithmetic, 'every composite number can be expressed (factorised) as a product of primes'

$\Rightarrow 2\times 3\times {13}^2$ is a composite number.