Prime Factorizatio

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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Is Number a Factor of Both - From Values as Factors

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Is 105 a factor of both 330 and 910?

\begin{align*}105 &= 3 \cdot 5 \cdot 7\\\\[-0.5em]330 &= 2 \cdot 3 \cdot 5 \cdot 11\\[-0.5em]910 &= 2 \cdot 5 \cdot 7 \cdot 13\end{align*}\\\\ \textsf{is }105\textsf{ a factor of}\\330\textsf{ and }910?

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

Math worksheet on 'Prime Factorization - Is Number a Factor of Both - From Values as Factors (Level 2)'. Part of a broader unit on 'Factoring and Venn Factor Diagrams - Practice' Learn online: app.mobius.academy/math/units/factoring_and_venn_diagrams_practice/

$A LaTex expression showing \begin{align*}12 &= 2 to the power of 2 times 3\\\\[-0.5em]60 &= 2 to the power of 2 times 3 times 5\\[-0.5em]84 &= 2 to the power of 2 times 3 times 7\end{align*}\\\\ \textsf{is }12\textsf{ a factor of}\\60\textsf{ and }84?$

Is 12 a factor of both 60 and 84?

Yes

$A LaTex expression showing \begin{align*}175 &= 5 to the power of 2 times 7\\\\[-0.5em]350 &= 2 times 5 to the power of 2 times 7\\[-0.5em]525 &= 3 times 5 to the power of 2 times 7\end{align*}\\\\ \textsf{is }175\textsf{ a factor of}\\350\textsf{ and }525?$

Is 175 a factor of both 350 and 525?

Yes

$A LaTex expression showing \begin{align*}98 &= 2 times 7 to the power of 2 \\\\[-0.5em]210 &= 2 times 3 times 5 times 7\\[-0.5em]1617 &= 3 times 7 to the power of 2 times 11\end{align*}\\\\ \textsf{is }98\textsf{ a factor of}\\210\textsf{ and }1617?$

Is 98 a factor of both 210 and 1617?

Yes

$A LaTex expression showing \begin{align*}28 &= 2 to the power of 2 times 7\\\\[-0.5em]84 &= 2 to the power of 2 times 3 times 7\\[-0.5em]140 &= 2 to the power of 2 times 5 times 7\end{align*}\\\\ \textsf{is }28\textsf{ a factor of}\\84\textsf{ and }140?$

Is 28 a factor of both 84 and 140?

Yes

$A LaTex expression showing \begin{align*}28 &= 2 to the power of 2 times 7\\\\[-0.5em]210 &= 2 times 3 times 5 times 7\\[-0.5em]132 &= 2 to the power of 2 times 3 times 11\end{align*}\\\\ \textsf{is }28\textsf{ a factor of}\\210\textsf{ and }132?$

Is 28 a factor of both 210 and 132?

Yes

$A LaTex expression showing \begin{align*}105 &= 3 times 5 times 7\\\\[-0.5em]770 &= 2 times 5 times 7 times 11\\[-0.5em]546 &= 2 times 3 times 7 times 13\end{align*}\\\\ \textsf{is }105\textsf{ a factor of}\\770\textsf{ and }546?$

Is 105 a factor of both 770 and 546?

Yes

$A LaTex expression showing \begin{align*}75 &= 3 times 5 to the power of 2 \\\\[-0.5em]150 &= 2 times 3 times 5 to the power of 2 \\[-0.5em]525 &= 3 times 5 to the power of 2 times 7\end{align*}\\\\ \textsf{is }75\textsf{ a factor of}\\150\textsf{ and }525?$

Is 75 a factor of both 150 and 525?

Yes

Prime Factorizatio

Practice:

Is Number a Factor of Both - From Values as Factors

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