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.
morePractice:
Is Number a Factor of Both - From Variables as Factors
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Is z a factor of both 98 and 147?
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Prime Factorization - Is Number a Factor of Both - From Variables as Factors Worksheet
| Math worksheet on 'Prime Factorization - Is Number a Factor of Both - From Variables as Factors (Level 1)'. Part of a broader unit on 'Factoring and Greatest Common Factor - Practice' Learn online: app.mobius.academy/math/units/factoring_and_greatest_common_factor_practice/ |
1
![A LaTex expression showing \begin{align*}b &= 2 to the power of 2 \\\\[-0.5em]30 &= 2 times 3 times 5\\[-0.5em]42 &= 2 times 3 times 7\end{align*}\\\\ \textsf{is }b\textsf{ a factor of}\\30\textsf{ and }42?](https://api.mobius.academy/storedimages/4907617/render)
| Is b a factor of both 30 and 42? |
a
| Yes |
b
| No |
2
![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?](https://api.mobius.academy/storedimages/4907615/render)
| Is m a factor of both 18 and 45? |
a
| Yes |
b
| No |
3
![A LaTex expression showing \begin{align*}z &= 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 }z\textsf{ a factor of}\\18\textsf{ and }45?](https://api.mobius.academy/storedimages/4907685/render)
| Is z a factor of both 18 and 45? |
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?](https://api.mobius.academy/storedimages/4907647/render)
| Is n a factor of both 42 and 105? |
a
| Yes |
b
| No |
5
![A LaTex expression showing \begin{align*}p &= 3 times 7\\\\[-0.5em]42 &= 2 times 3 times 7\\[-0.5em]105 &= 3 times 5 times 7\end{align*}\\\\ \textsf{is }p\textsf{ a factor of}\\42\textsf{ and }105?](https://api.mobius.academy/storedimages/4907624/render)
| Is p a factor of both 42 and 105? |
a
| Yes |
b
| No |
6
![A LaTex expression showing \begin{align*}z &= 3 times 5\\\\[-0.5em]70 &= 2 times 5 times 7\\[-0.5em]66 &= 2 times 3 times 11\end{align*}\\\\ \textsf{is }z\textsf{ a factor of}\\70\textsf{ and }66?](https://api.mobius.academy/storedimages/4907704/render)
| Is z a factor of both 70 and 66? |
a
| Yes |
b
| No |
7
![A LaTex expression showing \begin{align*}b &= 7 to the power of 2 \\\\[-0.5em]98 &= 2 times 7 to the power of 2 \\[-0.5em]147 &= 3 times 7 to the power of 2 \end{align*}\\\\ \textsf{is }b\textsf{ a factor of}\\98\textsf{ and }147?](https://api.mobius.academy/storedimages/4907604/render)
| Is b a factor of both 98 and 147? |
a
| Yes |
b
| No |