Question

Show that \(11 \times 19 \times 23 + 3 \times 11\) is not a prime number.

Answer 1

Step 1: Simplifying the given expression:

We are given the expression \( 11 \times 19 \times 23 + 3 \times 11 \) and asked to show that it is not a prime number.
First, we factor out \( 11 \) from both terms of the expression:
\[ 11 \times 19 \times 23 + 3 \times 11 = 11 \left( 19 \times 23 + 3 \right) \]

Step 2: Simplifying the terms inside the parentheses:

Now, simplify the expression inside the parentheses:
\[ 19 \times 23 = 437 \] \[ 19 \times 23 + 3 = 437 + 3 = 440 \] So, the expression becomes:
\[ 11 \times 440 \]

Step 3: Determining if the result is a prime number:

The result is \( 11 \times 440 \), which is a product of two numbers: 11 and 440. Since it is a product of two numbers greater than 1, the result is not a prime number.

Conclusion:

Thus, \( 11 \times 19 \times 23 + 3 \times 11 \) is not a prime number because it is the product of two factors, 11 and 440.