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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.

Is Number a Factor of Both - From Values as Factors

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Is 54 a factor of both 630 and 990?

54=2⋅33630=2⋅32⋅5⋅7990=2⋅32⋅5⋅11is 54 a factor of630 and 990?\begin{align*}54 &= 2 \cdot 3^3\\\\[-0.5em]630 &= 2 \cdot 3^2 \cdot 5 \cdot 7\\[-0.5em]990 &= 2 \cdot 3^2 \cdot 5 \cdot 11\end{align*}\\\\ \textsf{is }54\textsf{ a factor of}\\630\textsf{ and }990?