To explain why \(3 \times 5 \times 7 + 7\) is a composite number, we can follow these steps:
### Step 1: Calculate the expression \(3 \times 5 \times 7 + 7\)
First, we need to calculate the value of the expression.
1. Multiply \(3\), \(5\), and \(7\):
\[
3 \times 5 = 15
\]
\[
15 \times 7 = 105
\]
2. Now, add \(7\) to \(105\):
\[
105 + 7 = 112
\]
So, \(3 \times 5 \times 7 + 7 = 112\).
### Step 2: Define a composite number
A composite number is defined as a number that has more than two distinct positive factors. This means it can be divided evenly by numbers other than just \(1\) and itself.
### Step 3: Find the factors of \(112\)
Now, we need to find the factors of \(112\) to determine if it is composite.
1. Start with \(1\) (since every number is divisible by \(1\)):
- \(1\) is a factor of \(112\).
2. Check for divisibility by \(2\):
- \(112 \div 2 = 56\) (so \(2\) is a factor).
3. Continue checking for other factors:
- \(112 \div 4 = 28\) (so \(4\) is a factor).
- \(112 \div 7 = 16\) (so \(7\) is a factor).
- \(112 \div 8 = 14\) (so \(8\) is a factor).
- \(112 \div 14 = 8\) (already counted).
- \(112 \div 16 = 7\) (already counted).
- \(112 \div 28 = 4\) (already counted).
- \(112 \div 56 = 2\) (already counted).
- \(112 \div 112 = 1\) (already counted).
The complete list of factors of \(112\) is:
- \(1, 2, 4, 7, 8, 14, 16, 28, 56, 112\)
### Step 4: Count the factors
From the list, we can see that \(112\) has the following factors: \(1, 2, 4, 7, 8, 14, 16, 28, 56, 112\).
This gives us a total of **10 factors**.
### Conclusion
Since \(112\) has more than two factors, we conclude that \(112\) is a composite number. Therefore, \(3 \times 5 \times 7 + 7\) is a composite number.
### Summary
Thus, we can say:
\[
3 \times 5 \times 7 + 7 = 112 \text{ is a composite number because it has more than two factors.}
\]
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