# Explain why

Question:

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

Solution:

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

We can see that both the numbers have common factor 7 and 1.

$7 \times 11 \times 13+13=(77+1) \times 13$

$=78 \times 13$

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

$=1008 \times 5$

And we know that composite numbers are those numbers which have at least one more factor other than 1.

Hence after simplification we see that both numbers are even and therefore the given two numbers are composite numbers