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Prime Factorization

Is Number a Factor of Both - From Values as Factors (Level 2)

This math topic fosters understanding in prime factorization, factoring, and the utilization of greatest common factors. Students practice recognizing if a number is a factor of two other numbers via prime factorization represented in exponential form. The problems prompt students to determine whether a specific number can be a factor of two given numbers by examining their prime factorized forms and common factors. Each question also includes a binary choice (Yes or No) for the answers, guiding students to assess factorization results critically.

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 Values as Factors Worksheet

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Prime Factorization - Is Number a Factor of Both - From Values as Factors
1
A LaTex expression showing \begin{align*}98 &= 2 times 7 to the power of 2 \\\\[-0.5em]210 &= 2 times 3 times 5 times 7\\[-0.5em]1617 &= 3 times 7 to the power of 2 times 11\end{align*}\\\\ \textsf{is }98\textsf{ a factor of}\\210\textsf{ and }1617?
Is 98 a factor of both 210 and 1617?
a
Yes
b
No
2
A LaTex expression showing \begin{align*}45 &= 3 to the power of 2 times 5\\\\[-0.5em]90 &= 2 times 3 to the power of 2 times 5\\[-0.5em]315 &= 3 to the power of 2 times 5 times 7\end{align*}\\\\ \textsf{is }45\textsf{ a factor of}\\90\textsf{ and }315?
Is 45 a factor of both 90 and 315?
a
Yes
b
No
3
A LaTex expression showing \begin{align*}105 &= 3 times 5 times 7\\\\[-0.5em]462 &= 2 times 3 times 7 times 11\\[-0.5em]910 &= 2 times 5 times 7 times 13\end{align*}\\\\ \textsf{is }105\textsf{ a factor of}\\462\textsf{ and }910?
Is 105 a factor of both 462 and 910?
a
Yes
b
No
4
A LaTex expression showing \begin{align*}12 &= 2 to the power of 2 times 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 }12\textsf{ a factor of}\\60\textsf{ and }84?
Is 12 a factor of both 60 and 84?
a
Yes
b
No
5
A LaTex expression showing \begin{align*}30 &= 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 }30\textsf{ a factor of}\\210\textsf{ and }330?
Is 30 a factor of both 210 and 330?
a
Yes
b
No
6
A LaTex expression showing \begin{align*}28 &= 2 to the power of 2 times 7\\\\[-0.5em]210 &= 2 times 3 times 5 times 7\\[-0.5em]132 &= 2 to the power of 2 times 3 times 11\end{align*}\\\\ \textsf{is }28\textsf{ a factor of}\\210\textsf{ and }132?
Is 28 a factor of both 210 and 132?
a
Yes
b
No
7
A LaTex expression showing \begin{align*}30 &= 2 times 3 times 5\\\\[-0.5em]462 &= 2 times 3 times 7 times 11\\[-0.5em]546 &= 2 times 3 times 7 times 13\end{align*}\\\\ \textsf{is }30\textsf{ a factor of}\\462\textsf{ and }546?
Is 30 a factor of both 462 and 546?
a
Yes
b
No
8
A LaTex expression showing \begin{align*}28 &= 2 to the power of 2 times 7\\\\[-0.5em]84 &= 2 to the power of 2 times 3 times 7\\[-0.5em]140 &= 2 to the power of 2 times 5 times 7\end{align*}\\\\ \textsf{is }28\textsf{ a factor of}\\84\textsf{ and }140?
Is 28 a factor of both 84 and 140?
a
Yes
b
No