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Prime Factorization - Is Number a Multiple - From Value as Factors (Level 3)

This math topic focuses on advanced skills related to prime factorization, determining if one number is a multiple of another, and understanding value representations as factors. Specifically, it entails evaluating given numbers expressed in factorized forms, to ascertain if one is a multiple of another utilizing their prime factorization. The problems provide factorized expressions for two numbers and ask if the first is a multiple of the second, offering a deeper insight into factoring and lowest common multiples. The format includes multiple-choice answers to validate understanding.

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Is Number a Multiple - From Value as Factors

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Is 1050 a multiple of 510

1050=2⋅3⋅52⋅7510=2⋅3⋅5⋅17is 1050 a multiple of 510?\begin{align*}1050 &= 2 \cdot 3 \cdot 5^2 \cdot 7\\[-0.5em]510 &= 2 \cdot 3 \cdot 5 \cdot 17\end{align*}\\\\ \textsf{is }1050\textsf{ a multiple of }510?