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

This math topic focuses on advanced concepts of prime factorization and checking whether one number is a multiple of others, using their prime factorized forms. It involves determining if a primary number is a multiple of two other numbers by analyzing their factorized structures, as presented in the format of prime factors raised to appropriate exponents. Additionally, this topic falls under a broader unit on factoring and finding the lowest common multiple, targeting an advanced understanding of these concepts. Each problem presents a situation to decide if one number is a multiple of the others provided, with a choice of 'Yes' or 'No' as answers.

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

Is Number a Multiple of Both - From Values as Factors

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Is 700 a multiple of both 100 and 140?

700=22⋅52⋅7100=22⋅52140=22⋅5⋅7is 700 a multiple of 100 and 140?\begin{align*}700 &= 2^2 \cdot 5^2 \cdot 7\\[-0.5em]100 &= 2^2 \cdot 5^2\\[-0.5em]140 &= 2^2 \cdot 5 \cdot 7\end{align*}\\\\ \textsf{is }700\textsf{ a multiple of }\\100\textsf{ and }140?