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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.

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Is Number a Factor of Both - From Values as Factors

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Is 294 a factor of both 5390 and 9555?

294=2⋅3⋅725390=2⋅5⋅72⋅119555=3⋅5⋅72⋅13is 294 a factor of5390 and 9555?\begin{align*}294 &= 2 \cdot 3 \cdot 7^2\\\\[-0.5em]5390 &= 2 \cdot 5 \cdot 7^2 \cdot 11\\[-0.5em]9555 &= 3 \cdot 5 \cdot 7^2 \cdot 13\end{align*}\\\\ \textsf{is }294\textsf{ a factor of}\\5390\textsf{ and }9555?

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