3 Tutor System
Starting just at 265/hour

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

There are two types of number prime and composite
Prime numbers can be divided by 1 and only itself, whereas composite numbers have factors other than 1 and itself.
$$\therefore$$ $$7 × 11 × 13 + 13$$
= $$13 × (7 × 11 + 1)$$
= $$13 × (77 + 1)$$
= $$13 × 78 = 13 × 13 × 6$$
6 and 13 are the factors of $$7 × 11 × 13 + 13$$

And we know that numbers which have factors other than one and itself are composite number
$$7 × 6 × 5 × 4 × 3 × 2 × 1 + 5$$
=$$5 × (7 × 6 × 4 × 3 × 2 × 1 + 1)$$
= $$5 × (1008 + 1)$$
= $$5 × 1009$$

1009 is a prime number and cannot be factorized further

So, 5 and 1009 are the factors of $$7 × 6 × 5 × 4 × 3 × 2 × 1 + 5$$

And we know that numbers which have factors other than one and itself are composite number