Is 735 a factor of both 1470 and 8085? $$\begin{align*}735 &= 3 \cdot 5 \cdot 7^2\\\\[-0.5em]1470 &= 2 \cdot 3 \cdot 5 \cdot 7^2\\[-0.5em]8085 &= 3 \cdot 5 \cdot 7^2 \cdot 11\end{align*}\\\\ \textsf{is }735\textsf{ a factor of}\\1470\textsf{ and }8085?$$

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 150 a factor of both 5775 and 2730?

\begin{align*}150 &= 2 \cdot 3 \cdot 5^2\\\\[-0.5em]5775 &= 3 \cdot 5^2 \cdot 7 \cdot 11\\[-0.5em]2730 &= 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13\end{align*}\\\\ \textsf{is }150\textsf{ a factor of}\\5775\textsf{ and }2730?

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