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Prime Factorization - Is Integer a Factor of Both - From Values as Factors (Level 2)

This math topic focuses on prime factorization and explores whether specific integers are common factors of two given numbers. Each question presents the prime factorization of certain numbers and asks if a listed integer is a factor of both provided numbers. The integers and numbers are given in algebraic form, and the exercise helps strengthen understanding of factors, prime factorization, and the greatest common factor. This set of problems is suitable for those practicing factoring skills, specifically in identifying shared factors between numbers.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

Is Integer a Factor of Both - From Values as Factors

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Is 45 a factor of both 210 and 330?

45=x2⋅p210=2⋅3⋅5⋅7330=2⋅3⋅5⋅11is 45 a factor of210 and 330?\begin{align*}45 &= x^2 \cdot p\\[-0.5em]210 &= 2 \cdot 3 \cdot 5 \cdot 7\\[-0.5em]330 &= 2 \cdot 3 \cdot 5 \cdot 11\end{align*}\\\\ \textsf{is }45\textsf{ a factor of}\\210\textsf{ and }330?