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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.

Is Number a Factor of Both - From Values as Factors

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Is 40 a factor of both 420 and 660?

40=23⋅5420=22⋅3⋅5⋅7660=22⋅3⋅5⋅11is 40 a factor of420 and 660?\begin{align*}40 &= 2^3 \cdot 5\\[-0.5em]420 &= 2^2 \cdot 3 \cdot 5 \cdot 7\\[-0.5em]660 &= 2^2 \cdot 3 \cdot 5 \cdot 11\end{align*}\\\\ \textsf{is }40\textsf{ a factor of}\\420\textsf{ and }660?