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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.

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

Is 686 a factor of both 5145 and 3234?

686=2⋅735145=3⋅5⋅733234=2⋅3⋅72⋅11is 686 a factor of5145 and 3234?\begin{align*}686 &= 2 \cdot 7^3\\\\[-0.5em]5145 &= 3 \cdot 5 \cdot 7^3\\[-0.5em]3234 &= 2 \cdot 3 \cdot 7^2 \cdot 11\end{align*}\\\\ \textsf{is }686\textsf{ a factor of}\\5145\textsf{ and }3234?

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