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

This math topic focuses on evaluating the divisibility of numbers by examining prime factorization. It combines the concepts of factoring and finding the greatest common factor (GCF) in practical scenarios. Each question lists two expressions involving products of prime factors and asks whether one expression is a factor of the other two given expressions. The problems help enhance understanding of prime factorization, examining common factors, and applying these skills in finding whether one number is a factor of others. This is essential for developing skills in higher mathematics, particularly in algebra and number theory.

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 x a factor of both 210 and 462?

x=32⋅7210=2⋅3⋅5⋅7462=2⋅3⋅7⋅11is x a factor of210 and 462?\begin{align*}x &= 3^2 \cdot 7\\[-0.5em]210 &= 2 \cdot 3 \cdot 5 \cdot 7\\[-0.5em]462 &= 2 \cdot 3 \cdot 7 \cdot 11\end{align*}\\\\ \textsf{is }x\textsf{ a factor of}\\210\textsf{ and }462?

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 2)'. Part of a broader unit on 'Digits and Divisibility - Intro' Learn online: app.mobius.academy/math/units/digits_and_divisibility_intro/
1
A LaTex expression showing \begin{align*}z &= 2 times 3 times 5\\[-0.5em]462 &= 2 times 3 times 7 times 11\\[-0.5em]910 &= 2 times 5 times 7 times 13\end{align*}\\\\ \textsf{is }z\textsf{ a factor of}\\462\textsf{ and }910?
Is z a factor of both 462 and 910?
a
Yes
b
No
2
A LaTex expression showing \begin{align*}y &= 2 to the power of 3 \\[-0.5em]60 &= 2 to the power of 2 times 3 times 5\\[-0.5em]84 &= 2 to the power of 2 times 3 times 7\end{align*}\\\\ \textsf{is }y\textsf{ a factor of}\\60\textsf{ and }84?
Is y a factor of both 60 and 84?
a
Yes
b
No
3
A LaTex expression showing \begin{align*}x &= 3 to the power of 2 times 7\\[-0.5em]90 &= 2 times 3 to the power of 2 times 5\\[-0.5em]462 &= 2 times 3 times 7 times 11\end{align*}\\\\ \textsf{is }x\textsf{ a factor of}\\90\textsf{ and }462?
Is x a factor of both 90 and 462?
a
Yes
b
No
4
A LaTex expression showing \begin{align*}c &= 2 to the power of 3 \\[-0.5em]60 &= 2 to the power of 2 times 3 times 5\\[-0.5em]84 &= 2 to the power of 2 times 3 times 7\end{align*}\\\\ \textsf{is }c\textsf{ a factor of}\\60\textsf{ and }84?
Is c a factor of both 60 and 84?
a
Yes
b
No
5
A LaTex expression showing \begin{align*}y &= 2 times 3 times 5\\[-0.5em]210 &= 2 times 3 times 5 times 7\\[-0.5em]330 &= 2 times 3 times 5 times 11\end{align*}\\\\ \textsf{is }y\textsf{ a factor of}\\210\textsf{ and }330?
Is y a factor of both 210 and 330?
a
Yes
b
No
6
A LaTex expression showing \begin{align*}b &= 2 times 3 times 5\\[-0.5em]210 &= 2 times 3 times 5 times 7\\[-0.5em]330 &= 2 times 3 times 5 times 11\end{align*}\\\\ \textsf{is }b\textsf{ a factor of}\\210\textsf{ and }330?
Is b a factor of both 210 and 330?
a
Yes
b
No
7
A LaTex expression showing \begin{align*}m &= 2 times 5 times 7\\[-0.5em]462 &= 2 times 3 times 7 times 11\\[-0.5em]546 &= 2 times 3 times 7 times 13\end{align*}\\\\ \textsf{is }m\textsf{ a factor of}\\462\textsf{ and }546?
Is m a factor of both 462 and 546?
a
Yes
b
No