NCERT · Class 10 · Mathematics · Real NumbersExplain why $7 \times 11 \times 13 + 13$ is a composite number.

To show that the given expression is a composite number, we need to prove that it has factors other than 1 and itself. By taking 13 common from the given expression $7 \times 11 \times 13 + 13$, we get $13(7 \times 11 \times 1 + 1) = 13(77 + 1) = 13 \times 78$. Since the number can be expressed as a product of prime factors other than 1 and the number itself, it is definitely a composite number.