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

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Is n a multiple of both 147 and 105?

n=3572147=372105=357is n a multiple of 147 and 105?\begin{align*}n &= 3 \cdot 5 \cdot 7^2\\\\[-0.5em]147 &= 3 \cdot 7^2\\[-0.5em]105 &= 3 \cdot 5 \cdot 7\end{align*}\\\\ \textsf{is }n\textsf{ a multiple of }\\147\textsf{ and }105?

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

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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/
1
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?
a
Yes
b
No
2
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?
a
Yes
b
No
3
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?
a
Yes
b
No
4
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?
a
Yes
b
No
5
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?
a
Yes
b
No
6
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?
a
Yes
b
No
7
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?
a
Yes
b
No