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Prime Factorization - Is Number a Multiple of Both - From Variables as Factors (Level 3)

This math topic focuses on advanced skills related to prime factorization, particularly assessing if one number is a multiple of other numbers using variable factors and exponents. Participants determine if specific values of a variable (represented as products of primes and their powers) are multiples of given numbers. The problems employ factorization and concepts of lowest common multiples to analyze mathematical relationships and verify multiple conditions. Additionally, this includes practice in translating between numerical expressions and contextualizing mathematical statements.

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 m a multiple of both 315 and 735?

m=32⋅5⋅72315=32⋅5⋅7735=3⋅5⋅72is m a multiple of 315 and 735?\begin{align*}m &= 3^2 \cdot 5 \cdot 7^2\\[-0.5em]315 &= 3^2 \cdot 5 \cdot 7\\[-0.5em]735 &= 3 \cdot 5 \cdot 7^2\end{align*}\\\\ \textsf{is }m\textsf{ a multiple of }\\315\textsf{ and }735?

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 3)'. 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*}d &= 2 times 3 to the power of 2 times 5 to the power of 2 \\[-0.5em]90 &= 2 times 3 to the power of 2 times 5\\[-0.5em]150 &= 2 times 3 times 5 to the power of 2 \end{align*}\\\\ \textsf{is }d\textsf{ a multiple of }\\90\textsf{ and }150?
Is d a multiple of both 90 and 150?
a
Yes
b
No
2
A LaTex expression showing \begin{align*}c &= 2 to the power of 2 times 3 times 5 times 7\\[-0.5em]60 &= 2 to the power of 2 times 3 times 5\\[-0.5em]210 &= 2 times 3 times 5 times 7\end{align*}\\\\ \textsf{is }c\textsf{ a multiple of }\\60\textsf{ and }210?
Is c a multiple of both 60 and 210?
a
Yes
b
No
3
A LaTex expression showing \begin{align*}x &= 2 times 3 times 5 times 7 to the power of 2 \\[-0.5em]735 &= 3 times 5 times 7 to the power of 2 \\[-0.5em]210 &= 2 times 3 times 5 times 7\end{align*}\\\\ \textsf{is }x\textsf{ a multiple of }\\735\textsf{ and }210?
Is x a multiple of both 735 and 210?
a
Yes
b
No
4
A LaTex expression showing \begin{align*}x &= 2 times 3 times 5 to the power of 2 times 7\\[-0.5em]510 &= 2 times 3 times 5 times 17\\[-0.5em]150 &= 2 times 3 times 5 to the power of 2 \end{align*}\\\\ \textsf{is }x\textsf{ a multiple of }\\510\textsf{ and }150?
Is x a multiple of both 510 and 150?
a
Yes
b
No
5
A LaTex expression showing \begin{align*}r &= 3 to the power of 3 times 5 to the power of 2 \\[-0.5em]54 &= 2 times 3 to the power of 3 \\[-0.5em]135 &= 3 to the power of 3 times 5\end{align*}\\\\ \textsf{is }r\textsf{ a multiple of }\\54\textsf{ and }135?
Is r a multiple of both 54 and 135?
a
Yes
b
No
6
A LaTex expression showing \begin{align*}d &= 3 to the power of 2 times 5 to the power of 2 times 7\\[-0.5em]819 &= 3 to the power of 2 times 7 times 13\\[-0.5em]525 &= 3 times 5 to the power of 2 times 7\end{align*}\\\\ \textsf{is }d\textsf{ a multiple of }\\819\textsf{ and }525?
Is d a multiple of both 819 and 525?
a
Yes
b
No
7
A LaTex expression showing \begin{align*}x &= 3 times 5 to the power of 4 \\[-0.5em]375 &= 3 times 5 to the power of 3 \\[-0.5em]625 &= 5 to the power of 4 \end{align*}\\\\ \textsf{is }x\textsf{ a multiple of }\\375\textsf{ and }625?
Is x a multiple of both 375 and 625?
a
Yes
b
No