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Prime Factorization

Is Number a Factor of Both - From Variables as Factors (Level 1)

This math topic practices the skill of determining whether one number is a factor of other numbers, using prime factorization. Each problem presents prime factorizations of multiple numbers and asks if a specific factor is common to two given numbers. The learner must understand how to break numbers into their prime factors and check commonality between factorized forms.

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

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

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Prime Factorization - Is Number a Factor of Both - From Variables as Factors
1
A LaTex expression showing \begin{align*}z &= 3 times 7\\\\[-0.5em]42 &= 2 times 3 times 7\\[-0.5em]105 &= 3 times 5 times 7\end{align*}\\\\ \textsf{is }z\textsf{ a factor of}\\42\textsf{ and }105?
Is z a factor of both 42 and 105?
a
Yes
b
No
2
A LaTex expression showing \begin{align*}r &= 2 times 7\\\\[-0.5em]42 &= 2 times 3 times 7\\[-0.5em]70 &= 2 times 5 times 7\end{align*}\\\\ \textsf{is }r\textsf{ a factor of}\\42\textsf{ and }70?
Is r a factor of both 42 and 70?
a
Yes
b
No
3
A LaTex expression showing \begin{align*}r &= 3 times 7\\\\[-0.5em]70 &= 2 times 5 times 7\\[-0.5em]154 &= 2 times 7 times 11\end{align*}\\\\ \textsf{is }r\textsf{ a factor of}\\70\textsf{ and }154?
Is r a factor of both 70 and 154?
a
Yes
b
No
4
A LaTex expression showing \begin{align*}n &= 3 times 7\\\\[-0.5em]42 &= 2 times 3 times 7\\[-0.5em]105 &= 3 times 5 times 7\end{align*}\\\\ \textsf{is }n\textsf{ a factor of}\\42\textsf{ and }105?
Is n a factor of both 42 and 105?
a
Yes
b
No
5
A LaTex expression showing \begin{align*}z &= 2 times 5\\\\[-0.5em]30 &= 2 times 3 times 5\\[-0.5em]70 &= 2 times 5 times 7\end{align*}\\\\ \textsf{is }z\textsf{ a factor of}\\30\textsf{ and }70?
Is z a factor of both 30 and 70?
a
Yes
b
No
6
A LaTex expression showing \begin{align*}x &= 2 times 7\\\\[-0.5em]30 &= 2 times 3 times 5\\[-0.5em]66 &= 2 times 3 times 11\end{align*}\\\\ \textsf{is }x\textsf{ a factor of}\\30\textsf{ and }66?
Is x a factor of both 30 and 66?
a
Yes
b
No
7
A LaTex expression showing \begin{align*}y &= 2 times 5\\\\[-0.5em]105 &= 3 times 5 times 7\\[-0.5em]165 &= 3 times 5 times 11\end{align*}\\\\ \textsf{is }y\textsf{ a factor of}\\105\textsf{ and }165?
Is y a factor of both 105 and 165?
a
Yes
b
No
8
A LaTex expression showing \begin{align*}m &= 3 to the power of 2 \\\\[-0.5em]18 &= 2 times 3 to the power of 2 \\[-0.5em]45 &= 3 to the power of 2 times 5\end{align*}\\\\ \textsf{is }m\textsf{ a factor of}\\18\textsf{ and }45?
Is m a factor of both 18 and 45?
a
Yes
b
No