Explain why \(3 \times 5 \times 7 + 7\) is a composite number.
\(3 \times 5 \times 7 + 7 = 112\), and since \(112 = 7 \times 16\), it has more than two factors. Hence it is a composite number.
Step 1: Simplify the given expression.
We are asked to check if \(3 \times 5 \times 7 + 7\) is a composite number.
First calculate the product: \(3 \times 5 \times 7 = 105\).
Add 7: \(105 + 7 = 112\).
Step 2: Factorize the number.
Notice that we can factor 7 from the original expression:
\(3 \times 5 \times 7 + 7 = 7(3 \times 5 + 1)\).
Simplify inside the bracket: \(3 \times 5 + 1 = 15 + 1 = 16\).
So the number becomes \(7 \times 16\).
Step 3: Check for factors.
Since \(112 = 7 \times 16\), it is divisible by 7 and 16 in addition to 1 and 112.
This means it has more than two factors.
Conclusion. A number with more than two factors is a composite number. Therefore, 112 is composite.