Explain why $3 \times 5 \times 7 + 7$ is a composite number.

(N/A) We have,$3 \times 5 \times 7 + 7 = 105 + 7 = 112$.
Now,we find the prime factorization of $112$:
$112 = 2 \times 56 = 2 \times 2 \times 28 = 2 \times 2 \times 2 \times 14 = 2 \times 2 \times 2 \times 2 \times 7 = 2^4 \times 7$.
Since $112$ can be expressed as a product of prime factors $2$ and $7$,it has more than two factors (specifically,$1, 2, 4, 7, 8, 14, 16, 28, 56, 112$).
By definition,a number that has more than two factors is a composite number. Therefore,$3 \times 5 \times 7 + 7$ is a composite number.