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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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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 462 and 546?

105=3⋅5⋅7462=2⋅3⋅7⋅11546=2⋅3⋅7⋅13is 105 a factor of462 and 546?\begin{align*}105 &= 3 \cdot 5 \cdot 7\\[-0.5em]462 &= 2 \cdot 3 \cdot 7 \cdot 11\\[-0.5em]546 &= 2 \cdot 3 \cdot 7 \cdot 13\end{align*}\\\\ \textsf{is }105\textsf{ a factor of}\\462\textsf{ and }546?

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

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Math worksheet on 'Prime Factorization - Is Number a Factor of Both - From Values 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*}63 &= 3 to the power of 2 times 7\\[-0.5em]90 &= 2 times 3 to the power of 2 times 5\\[-0.5em]198 &= 2 times 3 to the power of 2 times 11\end{align*}\\\\ \textsf{is }63\textsf{ a factor of}\\90\textsf{ and }198?
Is 63 a factor of both 90 and 198?
a
Yes
b
No
2
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?
a
Yes
b
No
3
A LaTex expression showing \begin{align*}20 &= 2 to the power of 2 times 5\\[-0.5em]60 &= 2 to the power of 2 times 3 times 5\\[-0.5em]140 &= 2 to the power of 2 times 5 times 7\end{align*}\\\\ \textsf{is }20\textsf{ a factor of}\\60\textsf{ and }140?
Is 20 a factor of both 60 and 140?
a
Yes
b
No
4
A LaTex expression showing \begin{align*}50 &= 2 times 5 to the power of 2 \\[-0.5em]150 &= 2 times 3 times 5 to the power of 2 \\[-0.5em]350 &= 2 times 5 to the power of 2 times 7\end{align*}\\\\ \textsf{is }50\textsf{ a factor of}\\150\textsf{ and }350?
Is 50 a factor of both 150 and 350?
a
Yes
b
No
5
A LaTex expression showing \begin{align*}63 &= 3 to the power of 2 times 7\\[-0.5em]210 &= 2 times 3 times 5 times 7\\[-0.5em]462 &= 2 times 3 times 7 times 11\end{align*}\\\\ \textsf{is }63\textsf{ a factor of}\\210\textsf{ and }462?
Is 63 a factor of both 210 and 462?
a
Yes
b
No
6
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?
a
Yes
b
No
7
A LaTex expression showing \begin{align*}63 &= 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 }63\textsf{ a factor of}\\90\textsf{ and }462?
Is 63 a factor of both 90 and 462?
a
Yes
b
No