Explain why ` 3 xx 5xx 7 xx + 7` is a composite number

Answer

To determine why the expression \(3 \times 5 \times 7 \times 9 + 7\) is a composite number, we can follow these steps:

### Step 1: Calculate the expression
First, we need to simplify the expression \(3 \times 5 \times 7 \times 9 + 7\).

1. Calculate \(3 \times 5 = 15\).
2. Next, calculate \(15 \times 7 = 105\).
3. Then, calculate \(105 \times 9 = 945\).
4. Finally, add \(7\) to \(945\):
\[ 945 + 7 = 952 \]

So, the expression simplifies to \(952\).

### Step 2: Determine the factors of 952
Next, we need to find the factors of \(952\) to check if it is composite.

1. Since \(952\) is an even number, it is divisible by \(2\):
\[ 952 \div 2 = 476 \]
2. Continuing to divide by \(2\):
\[ 476 \div 2 = 238 \]
3. Again, divide by \(2\):
\[ 238 \div 2 = 119 \]
4. Now, \(119\) is not divisible by \(2\). We check the next prime number, \(3\) (it is not divisible), and then \(5\) (it is not divisible). Next, we check \(7\):
\[ 119 \div 7 = 17 \]

Now we have:
\[ 952 = 2^3 \times 7 \times 17 \]

### Step 3: Identify the factors of 952
From the factorization \(2^3 \times 7 \times 17\), we can determine the factors of \(952\):
- The factors include \(1\), \(2\), \(4\), \(8\), \(7\), \(14\), \(28\), \(17\), \(34\), \(68\), \(119\), \(238\), \(476\), and \(952\).

### Step 4: Conclusion
Since \(952\) has more than two factors (it has at least \(1\), \(2\), and itself), it is classified as a composite number.

### Summary
Thus, \(3 \times 5 \times 7 \times 9 + 7 = 952\) is a composite number because it has multiple factors other than \(1\) and itself.

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