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Prime Factorization - Is Number a Multiple of Both - From Variables as Factors (Level 3)

This math topic focuses on advanced skills related to prime factorization, particularly assessing if one number is a multiple of other numbers using variable factors and exponents. Participants determine if specific values of a variable (represented as products of primes and their powers) are multiples of given numbers. The problems employ factorization and concepts of lowest common multiples to analyze mathematical relationships and verify multiple conditions. Additionally, this includes practice in translating between numerical expressions and contextualizing mathematical statements.

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

Is Number a Multiple of Both - From Variables as Factors

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Is d a multiple of both 819 and 525?

d=32⋅52⋅7819=32⋅7⋅13525=3⋅52⋅7is d a multiple of 819 and 525?\begin{align*}d &= 3^2 \cdot 5^2 \cdot 7\\[-0.5em]819 &= 3^2 \cdot 7 \cdot 13\\[-0.5em]525 &= 3 \cdot 5^2 \cdot 7\end{align*}\\\\ \textsf{is }d\textsf{ a multiple of }\\819\textsf{ and }525?