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Prime Factorizatio

Is Number a Multiple of Both - From Variables as Factors (Level 2)

This math topic involves evaluating whether a given number \( z, r, y, b, m, r, \) or \( c \) is a multiple of two other specified numbers using prime factorization and variable exponents. Each question presents expressions where a number is expressed through a multiplication of primes raised to certain powers, and the student must determine if this number is a multiple of two others listed. This involves skills related to factoring, recognizing multiples, and working with lowest common multiples. Each question provides two answer choices: "Yes" or "No."

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Is Number a Multiple of Both - From Variables as Factors

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Is z a multiple of both 153 and 105?

z=32⋅5⋅7153=32⋅17105=3⋅5⋅7is z a multiple of 153 and 105?\begin{align*}z &= 3^2 \cdot 5 \cdot 7\\\\[-0.5em]153 &= 3^2 \cdot 17\\[-0.5em]105 &= 3 \cdot 5 \cdot 7\end{align*}\\\\ \textsf{is }z\textsf{ a multiple of }\\153\textsf{ and }105?

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