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Prime Factorization - Is Number a Factor of Both - From Variables as Factors (Level 2)

This math topic focuses on evaluating the divisibility of numbers by examining prime factorization. It combines the concepts of factoring and finding the greatest common factor (GCF) in practical scenarios. Each question lists two expressions involving products of prime factors and asks whether one expression is a factor of the other two given expressions. The problems help enhance understanding of prime factorization, examining common factors, and applying these skills in finding whether one number is a factor of others. This is essential for developing skills in higher mathematics, particularly in algebra and number theory.

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Is Number a Factor of Both - From Variables as Factors

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Is z a factor of both 150 and 350?

z=252150=2352350=2527is z a factor of150 and 350?\begin{align*}z &= 2 \cdot 5^2\\[-0.5em]150 &= 2 \cdot 3 \cdot 5^2\\[-0.5em]350 &= 2 \cdot 5^2 \cdot 7\end{align*}\\\\ \textsf{is }z\textsf{ a factor of}\\150\textsf{ and }350?