Is y a multiple of both 28 and 70? $$\begin{align*}y &= 2^2 \cdot 5 \cdot 7\\\\[-0.5em]28 &= 2^2 \cdot 7\\[-0.5em]70 &= 2 \cdot 5 \cdot 7\end{align*}\\\\ \textsf{is }y\textsf{ a multiple of }\\28\textsf{ and }70?$$

Prime Factorization

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."

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

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Is Number a Multiple of Both - From Variables as Factors

Is p a multiple of both 105 and 175?

\begin{align*}p &= 5^3 \cdot 7\\\\[-0.5em]105 &= 3 \cdot 5 \cdot 7\\[-0.5em]175 &= 5^2 \cdot 7\end{align*}\\\\ \textsf{is }p\textsf{ a multiple of }\\105\textsf{ and }175?

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