We observe the given expression 5 × 7 × 11 + 11. Both terms, (5 × 7 × 11) and 11, share a common factor of 11. Using the distributive property, we factor out 11.

Evaluating the terms inside the parentheses gives 5 × 7 = 35, and adding 1 yields 36. Therefore, the given expression simplifies to the product 11 × 36.

What is the common prime factor greater than 1 that can be taken out to show that $5 \times 7 \times 11 + 11$ is a composite number?

Answer: 11

Step-by-step solution

Step 1: Factor out the common term

We observe the given expression $5 \times 7 \times 11 + 11$ . Both terms, $(5 \times 7 \times 11)$ and $11$ , share a common factor of $11$ . Using the distributive property, we factor out $11$ .

Step 2: Simplify the expression inside the bracket

Evaluating the terms inside the parentheses gives $5 \times 7 = 35$ , and adding $1$ yields $36$ . Therefore, the given expression simplifies to the product $11 \times 36$ .

Step 3: Conclude that the number is composite

Since the expression can be written as a product of factors other than $1$ and itself, having $11$ as a prime factor, it is a composite number by the Fundamental Theorem of Arithmetic. The common prime factor taken out is $11$ .

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What is the common prime factor greater than 1 that can be taken out to show that 5×7×11+115 \times 7 \times 11 + 115×7×11+11 is a composite number?

Step-by-step solution

Step 1: Factor out the common term

Step 2: Simplify the expression inside the bracket

Step 3: Conclude that the number is composite

What is the common prime factor greater than 1 that can be taken out to show that $5 \times 7 \times 11 + 11$ is a composite number?