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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 210 a factor of both 2310 and 2730?

210=2⋅3⋅5⋅72310=2⋅3⋅5⋅7⋅112730=2⋅3⋅5⋅7⋅13is 210 a factor of2310 and 2730?\begin{align*}210 &= 2 \cdot 3 \cdot 5 \cdot 7\\\\[-0.5em]2310 &= 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11\\[-0.5em]2730 &= 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13\end{align*}\\\\ \textsf{is }210\textsf{ a factor of}\\2310\textsf{ and }2730?