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

This math topic focuses on advanced skills in prime factorization, specifically determining if a number is a factor of two other numbers using their prime factorizations. Each problem presents a factor and two products, expressed in prime factorized form, and asks students to determine if the given factor is indeed a factor of both products. The choices provided for each question are simply "Yes" or "No." This set of problems is part of a broader unit exploring Factoring and the Greatest Common Factor at an advanced level.

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

Is Number a Factor of Both - From Values as Factors

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Is 315 a factor of both 630 and 3465?

315=32⋅5⋅7630=2⋅32⋅5⋅73465=32⋅5⋅7⋅11is 315 a factor of630 and 3465?\begin{align*}315 &= 3^2 \cdot 5 \cdot 7\\[-0.5em]630 &= 2 \cdot 3^2 \cdot 5 \cdot 7\\[-0.5em]3465 &= 3^2 \cdot 5 \cdot 7 \cdot 11\end{align*}\\\\ \textsf{is }315\textsf{ a factor of}\\630\textsf{ and }3465?