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Prime Factorization - Is Integer a Factor of Both - From Values as Factors (Level 1)

This math topic focuses on the skills of prime factorization and evaluating if one integer is a factor of two other integers. The problems require identifying the factors of given numbers, represented in prime factorization, and determining whether a specific integer, also given in a factored form, is a common factor of both numbers. The exercises are structured to enhance understanding of factoring and the concept of the greatest common factor. Each problem presents two numbers with their prime factors listed and asks whether a given integer is a factor of both.

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Is Integer a Factor of Both - From Values as Factors

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Is 15 a factor of both 70 and 110?

15=xr70=257110=2511is 15 a factor of70 and 110?\begin{align*}15 &= x \cdot r\\[-0.5em]70 &= 2 \cdot 5 \cdot 7\\[-0.5em]110 &= 2 \cdot 5 \cdot 11\end{align*}\\\\ \textsf{is }15\textsf{ a factor of}\\70\textsf{ and }110?