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 1715 a factor of both 3430 and 5145?

1715=5⋅733430=2⋅5⋅735145=3⋅5⋅73is 1715 a factor of3430 and 5145?\begin{align*}1715 &= 5 \cdot 7^3\\\\[-0.5em]3430 &= 2 \cdot 5 \cdot 7^3\\[-0.5em]5145 &= 3 \cdot 5 \cdot 7^3\end{align*}\\\\ \textsf{is }1715\textsf{ a factor of}\\3430\textsf{ and }5145?

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