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

This math topic focuses on advanced factoring and determining if one number is a factor of another using prime factorization. It delves into comparing the prime factors of two numbers to establish whether one number can completely divide the other without leaving a remainder. Each problem presents two numbers with their prime factorizations and asks if the first number is a factor of the second. The implicit skills practiced include prime factorization, understanding exponents in prime factors, and fundamental divisibility rules within the context of advanced factoring and greatest common factors.

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Is Number a Factor - From Value as Factors

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Is 189 a factor of 378

189=33⋅7378=2⋅33⋅7is 189 a factor of378?\begin{align*}189 &= 3^3 \cdot 7\\[-0.5em]378 &= 2 \cdot 3^3 \cdot 7\end{align*}\\\\ \textsf{is }189\textsf{ a factor of}\\378?