Question

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

Answer 1

Step 1: Understanding the problem:
We are given the expression \( 11 \times 19 \times 23 + 3 \times 11 \), and we are asked to show that it is not a prime number.

Step 2: Factor the given expression:
First, observe that both terms in the expression contain \( 11 \) as a common factor. So, we can factor out \( 11 \) from the expression:
\[ 11 \times 19 \times 23 + 3 \times 11 = 11 \left( 19 \times 23 + 3 \right) \] Now, simplify the expression inside the parentheses:
\[ 19 \times 23 = 437 \] \[ 437 + 3 = 440 \] So, the expression becomes:
\[ 11 \times 440 \]

Step 3: Checking the result:
Now we have the product \( 11 \times 440 \). Since this is a product of two numbers, \( 11 \) and \( 440 \), it cannot be a prime number because a prime number is only divisible by 1 and itself.

Step 4: Conclusion:
Since \( 11 \times 440 \) is a product of two numbers, it is not a prime number. Therefore, \( 11 \times 19 \times 23 + 3 \times 11 \) is not a prime number.