Question

sort the expressions.
7x 15 13
factors of 15·13 factors of 7x

Explanation:

Step1: Analyze Factors of \(15 \cdot 13\)

The product \(15 \cdot 13\) has factors that are the numbers being multiplied, so 15 and 13 are factors of \(15 \cdot 13\).

Step2: Analyze Factors of \(7x\)

The expression \(7x\) is a product of 7 and \(x\), so the factors of \(7x\) are 7 and \(x\), but from the given options, \(7x\) itself? Wait, no, the given expressions are \(7x\), 15, 13. Wait, actually, the factors of \(15 \cdot 13\) are 15 and 13 (since \(15 \times 13 = 15 \cdot 13\), so 15 and 13 are factors). The factors of \(7x\) would be 7 and \(x\), but the given expression is \(7x\), so the factor of \(7x\) from the options is \(7x\)? Wait, no, let's re - check. The problem is to sort the expressions \(7x\), 15, 13 into "Factors of \(15 \cdot 13\)" and "Factors of \(7x\)".

For "Factors of \(15 \cdot 13\)": Since \(15\times13 = 15\cdot13\), the factors of \(15\cdot13\) (among the given expressions) are 15 and 13.

For "Factors of \(7x\)": Since \(7x=7\times x\), the factor of \(7x\) (among the given expressions) is \(7x\) (or 7 and \(x\), but \(x\) is not given, so from the given expressions, \(7x\) is the expression which is a product, and its factor (in the given set) is \(7x\)? Wait, no, the factors of a product \(ab\) are \(a\) and \(b\). So for \(7x\), the factors are 7 and \(x\), but since we have \(7x\) as an expression, and the other expressions are 15 and 13. So:

• Factors of \(15\cdot13\): 15, 13 (because \(15\times13 = 15\cdot13\), so 15 and 13 are factors of the product \(15\cdot13\))
• Factors of \(7x\): \(7x\) (since \(7x = 7\times x\), and \(7x\) is the product, and among the given expressions, \(7x\) is the expression that represents the product, so it's a factor? Wait, no, actually, the factors of \(7x\) are 7 and \(x\), but since we have \(7x\) as an expression, and the other options are 15 and 13 which are not factors of \(7x\) (unless \(x\) is 15 or 13, but we don't know that). So we sort:

"Factors of \(15\cdot13\)": 15, 13

"Factors of \(7x\)": \(7x\)

Answer:

• Factors of \(15 \cdot 13\): 15, 13
• Factors of \(7x\): \(7x\)