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.

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Is Number a Factor of Both - From Values as Factors

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Is 350 a factor of both 1650 and 1950?

350=25271650=2352111950=235213is 350 a factor of1650 and 1950?\begin{align*}350 &= 2 \cdot 5^2 \cdot 7\\\\[-0.5em]1650 &= 2 \cdot 3 \cdot 5^2 \cdot 11\\[-0.5em]1950 &= 2 \cdot 3 \cdot 5^2 \cdot 13\end{align*}\\\\ \textsf{is }350\textsf{ a factor of}\\1650\textsf{ and }1950?

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