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Prime Factorization - Is Number a Factor of Both - From Variables as Factors (Level 1)

This math topic practices the skill of determining whether one number is a factor of other numbers, using prime factorization. Each problem presents prime factorizations of multiple numbers and asks if a specific factor is common to two given numbers. The learner must understand how to break numbers into their prime factors and check commonality between factorized forms.

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Is Number a Factor of Both - From Variables as Factors

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Is d a factor of both 30 and 42?

d=2330=23542=237is d a factor of30 and 42?\begin{align*}d &= 2 \cdot 3\\[-0.5em]30 &= 2 \cdot 3 \cdot 5\\[-0.5em]42 &= 2 \cdot 3 \cdot 7\end{align*}\\\\ \textsf{is }d\textsf{ a factor of}\\30\textsf{ and }42?