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Prime Factorizatio

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.

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Is Number a Multiple of Both - From Variables as Factors

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Is p a multiple of both 1617 and 2401?

p=3⋅741617=3⋅72⋅112401=74is p a multiple of 1617 and 2401?\begin{align*}p &= 3 \cdot 7^4\\\\[-0.5em]1617 &= 3 \cdot 7^2 \cdot 11\\[-0.5em]2401 &= 7^4\end{align*}\\\\ \textsf{is }p\textsf{ a multiple of }\\1617\textsf{ and }2401?

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