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Prime Factorization - Is Number a Factor of Both - From Values as Factors (Level 2)

This math topic fosters understanding in prime factorization, factoring, and the utilization of greatest common factors. Students practice recognizing if a number is a factor of two other numbers via prime factorization represented in exponential form. The problems prompt students to determine whether a specific number can be a factor of two given numbers by examining their prime factorized forms and common factors. Each question also includes a binary choice (Yes or No) for the answers, guiding students to assess factorization results critically.

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 98 a factor of both 294 and 490?

98=2⋅72294=2⋅3⋅72490=2⋅5⋅72is 98 a factor of294 and 490?\begin{align*}98 &= 2 \cdot 7^2\\[-0.5em]294 &= 2 \cdot 3 \cdot 7^2\\[-0.5em]490 &= 2 \cdot 5 \cdot 7^2\end{align*}\\\\ \textsf{is }98\textsf{ a factor of}\\294\textsf{ and }490?