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Prime Factorizatio

Is Integer a Factor of Both - From Values as Factors (Level 3)

This math topic focuses on advanced factoring skills and the determination of common factors in different numbers. It employs prime factorization to assess whether a given integer is a factor of two other numbers. Problems present equations involving exponentiation and multiplication of prime numbers, requiring students to decide if one number is a factor of the others listed. Each question is structured with two potential answers: "Yes" or "No." This analysis aids students in understanding factor relationships and the concept of the greatest common factor at a deeper level.

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Is Integer a Factor of Both - From Values as Factors

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Is 56 a factor of both 420 and 924?

56=p3⋅z420=22⋅3⋅5⋅7924=22⋅3⋅7⋅11is 56 a factor of420 and 924?\begin{align*}56 &= p^3 \cdot z\\\\[-0.5em]420 &= 2^2 \cdot 3 \cdot 5 \cdot 7\\[-0.5em]924 &= 2^2 \cdot 3 \cdot 7 \cdot 11\end{align*}\\\\ \textsf{is }56\textsf{ a factor of}\\420\textsf{ and }924?

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