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.

View Unit

Is Number a Multiple of Both - From Variables as Factors

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Is y a multiple of both 70 and 175?

\begin{align*}y &= 5^2 \cdot 7^2\\\\[-0.5em]70 &= 2 \cdot 5 \cdot 7\\[-0.5em]175 &= 5^2 \cdot 7\end{align*}\\\\ \textsf{is }y\textsf{ a multiple of }\\70\textsf{ and }175?

Prime Factorization - Is Number a Multiple of Both - From Variables as Factors Worksheet

Math worksheet on 'Prime Factorization - Is Number a Multiple of Both - From Variables as Factors (Level 2)'. Part of a broader unit on 'Factoring and Lowest Common Multiple - Practice' Learn online: app.mobius.academy/math/units/factoring_and_lowest_common_multiple_practice/

$A LaTex expression showing \begin{align*}m &= 2 times 3 to the power of 2 times 7\\\\[-0.5em]18 &= 2 times 3 to the power of 2 \\[-0.5em]42 &= 2 times 3 times 7\end{align*}\\\\ \textsf{is }m\textsf{ a multiple of }\\18\textsf{ and }42?$

Is m a multiple of both 18 and 42?

Yes

$A LaTex expression showing \begin{align*}b &= 2 times 3 to the power of 2 times 5\\\\[-0.5em]45 &= 3 to the power of 2 times 5\\[-0.5em]18 &= 2 times 3 to the power of 2 \end{align*}\\\\ \textsf{is }b\textsf{ a multiple of }\\45\textsf{ and }18?$

Is b a multiple of both 45 and 18?

Yes

$A LaTex expression showing \begin{align*}c &= 2 to the power of 2 times 7 to the power of 2 \\\\[-0.5em]98 &= 2 times 7 to the power of 2 \\[-0.5em]28 &= 2 to the power of 2 times 7\end{align*}\\\\ \textsf{is }c\textsf{ a multiple of }\\98\textsf{ and }28?$

Is c a multiple of both 98 and 28?

Yes

$A LaTex expression showing \begin{align*}d &= 3 times 5 times 7 to the power of 2 \\\\[-0.5em]245 &= 5 times 7 to the power of 2 \\[-0.5em]105 &= 3 times 5 times 7\end{align*}\\\\ \textsf{is }d\textsf{ a multiple of }\\245\textsf{ and }105?$

Is d a multiple of both 245 and 105?

Yes

$A LaTex expression showing \begin{align*}n &= 2 times 3 times 5 times 7\\\\[-0.5em]105 &= 3 times 5 times 7\\[-0.5em]42 &= 2 times 3 times 7\end{align*}\\\\ \textsf{is }n\textsf{ a multiple of }\\105\textsf{ and }42?$

Is n a multiple of both 105 and 42?

Yes

$A LaTex expression showing \begin{align*}y &= 5 to the power of 2 times 7 to the power of 2 \\\\[-0.5em]70 &= 2 times 5 times 7\\[-0.5em]175 &= 5 to the power of 2 times 7\end{align*}\\\\ \textsf{is }y\textsf{ a multiple of }\\70\textsf{ and }175?$

Is y a multiple of both 70 and 175?

Yes

$A LaTex expression showing \begin{align*}r &= 2 times 3 times 7 to the power of 2 \\\\[-0.5em]66 &= 2 times 3 times 11\\[-0.5em]147 &= 3 times 7 to the power of 2 \end{align*}\\\\ \textsf{is }r\textsf{ a multiple of }\\66\textsf{ and }147?$

Is r a multiple of both 66 and 147?

Yes

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

Practice:

Is Number a Multiple of Both - From Variables as Factors

Prime Factorization - Is Number a Multiple of Both - From Variables as Factors Worksheet