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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

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

Is x a multiple of both 245 and 147?

x=3⋅5⋅72245=5⋅72147=3⋅72is x a multiple of 245 and 147?\begin{align*}x &= 3 \cdot 5 \cdot 7^2\\[-0.5em]245 &= 5 \cdot 7^2\\[-0.5em]147 &= 3 \cdot 7^2\end{align*}\\\\ \textsf{is }x\textsf{ a multiple of }\\245\textsf{ and }147?

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 - Advanced' Learn online: app.mobius.academy/math/units/factoring_and_lowest_common_multiple_advanced/
1
A LaTex expression showing \begin{align*}c &= 3 to the power of 2 times 7 to the power of 2 \\[-0.5em]45 &= 3 to the power of 2 times 5\\[-0.5em]147 &= 3 times 7 to the power of 2 \end{align*}\\\\ \textsf{is }c\textsf{ a multiple of }\\45\textsf{ and }147?
Is c a multiple of both 45 and 147?
a
Yes
b
No
2
A LaTex expression showing \begin{align*}r &= 2 to the power of 2 times 5 to the power of 2 \\[-0.5em]20 &= 2 to the power of 2 times 5\\[-0.5em]50 &= 2 times 5 to the power of 2 \end{align*}\\\\ \textsf{is }r\textsf{ a multiple of }\\20\textsf{ and }50?
Is r a multiple of both 20 and 50?
a
Yes
b
No
3
A LaTex expression showing \begin{align*}z &= 2 to the power of 2 times 5 times 7\\[-0.5em]30 &= 2 times 3 times 5\\[-0.5em]28 &= 2 to the power of 2 times 7\end{align*}\\\\ \textsf{is }z\textsf{ a multiple of }\\30\textsf{ and }28?
Is z a multiple of both 30 and 28?
a
Yes
b
No
4
A LaTex expression showing \begin{align*}r &= 3 to the power of 3 times 7\\[-0.5em]63 &= 3 to the power of 2 times 7\\[-0.5em]27 &= 3 to the power of 3 \end{align*}\\\\ \textsf{is }r\textsf{ a multiple of }\\63\textsf{ and }27?
Is r a multiple of both 63 and 27?
a
Yes
b
No
5
A LaTex expression showing \begin{align*}r &= 3 to the power of 2 times 5 times 7\\[-0.5em]99 &= 3 to the power of 2 times 11\\[-0.5em]63 &= 3 to the power of 2 times 7\end{align*}\\\\ \textsf{is }r\textsf{ a multiple of }\\99\textsf{ and }63?
Is r a multiple of both 99 and 63?
a
Yes
b
No
6
A LaTex expression showing \begin{align*}d &= 3 to the power of 2 times 5 times 7\\[-0.5em]70 &= 2 times 5 times 7\\[-0.5em]63 &= 3 to the power of 2 times 7\end{align*}\\\\ \textsf{is }d\textsf{ a multiple of }\\70\textsf{ and }63?
Is d a multiple of both 70 and 63?
a
Yes
b
No
7
A LaTex expression showing \begin{align*}m &= 3 times 5 times 7 to the power of 2 \\[-0.5em]147 &= 3 times 7 to the power of 2 \\[-0.5em]245 &= 5 times 7 to the power of 2 \end{align*}\\\\ \textsf{is }m\textsf{ a multiple of }\\147\textsf{ and }245?
Is m a multiple of both 147 and 245?
a
Yes
b
No