Explain why: `11xx13xx17+17` is a composite number.

Answer

To determine why the expression \( 11 \times 13 \times 17 + 17 \) is a composite number, we can follow these steps:

### Step 1: Identify the expression
The expression we are working with is:
\[ 11 \times 13 \times 17 + 17 \]

### Step 2: Factor out the common term
Notice that \( 17 \) is a common factor in both terms of the expression. We can factor \( 17 \) out:
\[ 17 \times (11 \times 13 + 1) \]

### Step 3: Simplify the expression inside the parentheses
Now, we need to calculate \( 11 \times 13 + 1 \):
\[ 11 \times 13 = 143 \]
So, we have:
\[ 11 \times 13 + 1 = 143 + 1 = 144 \]

### Step 4: Rewrite the expression
Now we can rewrite our expression as:
\[ 17 \times 144 \]

### Step 5: Determine the nature of the number
Since \( 17 \) is a prime number and \( 144 \) is a composite number (as it has factors other than 1 and itself), the product \( 17 \times 144 \) will also be a composite number.

### Conclusion
Thus, \( 11 \times 13 \times 17 + 17 \) is a composite number because it can be expressed as the product of two numbers, \( 17 \) and \( 144 \), both of which have more than two factors.

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