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Prime Factorization - Is Number a Factor of Both - From Variables as Factors (Level 3)

This math topic involves advanced exercises in factorization, specifically focusing on prime factorization and determining the greatest common factor. The exercises require students to determine whether a given number is a factor of two other numbers, using prime factorizations provided in algebraic form. Variables are incorporated to represent specific numeric values, combining learning about variables as factors with hands-on prime factorization practice. Each problem presents a situation where students decide if one number (represented by a variable) is a common factor of two different products, enhancing their skills in algebraic manipulation and understanding of factors.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

Is Number a Factor of Both - From Variables as Factors

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Is r a factor of both 630 and 1386?

r=2⋅32⋅7630=2⋅32⋅5⋅71386=2⋅32⋅7⋅11is r a factor of630 and 1386?\begin{align*}r &= 2 \cdot 3^2 \cdot 7\\[-0.5em]630 &= 2 \cdot 3^2 \cdot 5 \cdot 7\\[-0.5em]1386 &= 2 \cdot 3^2 \cdot 7 \cdot 11\end{align*}\\\\ \textsf{is }r\textsf{ a factor of}\\630\textsf{ and }1386?