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

This math topic involves advanced exercises in factorization, specifically focusing on prime factorization and determining the greatest common factor. The exercises require students to determine whether a given number is a factor of two other numbers, using prime factorizations provided in algebraic form. Variables are incorporated to represent specific numeric values, combining learning about variables as factors with hands-on prime factorization practice. Each problem presents a situation where students decide if one number (represented by a variable) is a common factor of two different products, enhancing their skills in algebraic manipulation and understanding of factors.

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

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Is Number a Factor of Both - From Variables as Factors

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Is d a factor of both 2310 and 1820?

d=22⋅3⋅72310=2⋅3⋅5⋅7⋅111820=22⋅5⋅7⋅13is d a factor of2310 and 1820?\begin{align*}d &= 2^2 \cdot 3 \cdot 7\\[-0.5em]2310 &= 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11\\[-0.5em]1820 &= 2^2 \cdot 5 \cdot 7 \cdot 13\end{align*}\\\\ \textsf{is }d\textsf{ a factor of}\\2310\textsf{ and }1820?

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

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Math worksheet on 'Prime Factorization - Is Number a Factor of Both - From Variables as Factors (Level 3)'. Part of a broader unit on 'Factoring and Greatest Common Factor - Advanced' Learn online: app.mobius.academy/math/units/factoring_and_greatest_common_factor_advanced/
1
A LaTex expression showing \begin{align*}d &= 2 to the power of 2 times 3 times 7\\[-0.5em]2310 &= 2 times 3 times 5 times 7 times 11\\[-0.5em]1820 &= 2 to the power of 2 times 5 times 7 times 13\end{align*}\\\\ \textsf{is }d\textsf{ a factor of}\\2310\textsf{ and }1820?
Is d a factor of both 2310 and 1820?
a
Yes
b
No
2
A LaTex expression showing \begin{align*}m &= 2 to the power of 2 times 5 to the power of 2 \\[-0.5em]1050 &= 2 times 3 times 5 to the power of 2 times 7\\[-0.5em]1650 &= 2 times 3 times 5 to the power of 2 times 11\end{align*}\\\\ \textsf{is }m\textsf{ a factor of}\\1050\textsf{ and }1650?
Is m a factor of both 1050 and 1650?
a
Yes
b
No
3
A LaTex expression showing \begin{align*}d &= 2 to the power of 2 times 3 times 5\\[-0.5em]924 &= 2 to the power of 2 times 3 times 7 times 11\\[-0.5em]1092 &= 2 to the power of 2 times 3 times 7 times 13\end{align*}\\\\ \textsf{is }d\textsf{ a factor of}\\924\textsf{ and }1092?
Is d a factor of both 924 and 1092?
a
Yes
b
No
4
A LaTex expression showing \begin{align*}m &= 2 times 5 times 7 to the power of 2 \\[-0.5em]1470 &= 2 times 3 times 5 times 7 to the power of 2 \\[-0.5em]5390 &= 2 times 5 times 7 to the power of 2 times 11\end{align*}\\\\ \textsf{is }m\textsf{ a factor of}\\1470\textsf{ and }5390?
Is m a factor of both 1470 and 5390?
a
Yes
b
No
5
A LaTex expression showing \begin{align*}m &= 2 times 3 times 7 to the power of 2 \\[-0.5em]1470 &= 2 times 3 times 5 times 7 to the power of 2 \\[-0.5em]3234 &= 2 times 3 times 7 to the power of 2 times 11\end{align*}\\\\ \textsf{is }m\textsf{ a factor of}\\1470\textsf{ and }3234?
Is m a factor of both 1470 and 3234?
a
Yes
b
No
6
A LaTex expression showing \begin{align*}x &= 2 to the power of 2 times 3 times 5\\[-0.5em]420 &= 2 to the power of 2 times 3 times 5 times 7\\[-0.5em]660 &= 2 to the power of 2 times 3 times 5 times 11\end{align*}\\\\ \textsf{is }x\textsf{ a factor of}\\420\textsf{ and }660?
Is x a factor of both 420 and 660?
a
Yes
b
No
7
A LaTex expression showing \begin{align*}n &= 2 to the power of 2 times 7 to the power of 2 \\[-0.5em]588 &= 2 to the power of 2 times 3 times 7 to the power of 2 \\[-0.5em]980 &= 2 to the power of 2 times 5 times 7 to the power of 2 \end{align*}\\\\ \textsf{is }n\textsf{ a factor of}\\588\textsf{ and }980?
Is n a factor of both 588 and 980?
a
Yes
b
No