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Prime Factorization - Is Number a Factor of Both - From Values as Factors (Level 3)

This math topic focuses on advanced skills in prime factorization, specifically determining if a number is a factor of two other numbers using their prime factorizations. Each problem presents a factor and two products, expressed in prime factorized form, and asks students to determine if the given factor is indeed a factor of both products. The choices provided for each question are simply "Yes" or "No." This set of problems is part of a broader unit exploring Factoring and the Greatest Common Factor at an advanced level.

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 210 a factor of both 6006 and 19635?

210=2⋅3⋅5⋅76006=2⋅3⋅7⋅11⋅1319635=3⋅5⋅7⋅11⋅17is 210 a factor of6006 and 19635?\begin{align*}210 &= 2 \cdot 3 \cdot 5 \cdot 7\\[-0.5em]6006 &= 2 \cdot 3 \cdot 7 \cdot 11 \cdot 13\\[-0.5em]19635 &= 3 \cdot 5 \cdot 7 \cdot 11 \cdot 17\end{align*}\\\\ \textsf{is }210\textsf{ a factor of}\\6006\textsf{ and }19635?

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 3)'. Part of a broader unit on 'Factoring and Greatest Common Factor - Advanced' Learn online: app.mobius.academy/math/units/factoring_and_greatest_common_factor_advanced/
1
A LaTex expression showing \begin{align*}1715 &= 5 times 7 to the power of 3 \\[-0.5em]3430 &= 2 times 5 times 7 to the power of 3 \\[-0.5em]5145 &= 3 times 5 times 7 to the power of 3 \end{align*}\\\\ \textsf{is }1715\textsf{ a factor of}\\3430\textsf{ and }5145?
Is 1715 a factor of both 3430 and 5145?
a
Yes
b
No
2
A LaTex expression showing \begin{align*}40 &= 2 to the power of 3 times 5\\[-0.5em]420 &= 2 to the power of 2 times 3 times 5 times 7\\[-0.5em]660 &= 2 to the power of 2 times 3 times 5 times 11\end{align*}\\\\ \textsf{is }40\textsf{ a factor of}\\420\textsf{ and }660?
Is 40 a factor of both 420 and 660?
a
Yes
b
No
3
A LaTex expression showing \begin{align*}294 &= 2 times 3 times 7 to the power of 2 \\[-0.5em]1470 &= 2 times 3 times 5 times 7 to the power of 2 \\[-0.5em]3234 &= 2 times 3 times 7 to the power of 2 times 11\end{align*}\\\\ \textsf{is }294\textsf{ a factor of}\\1470\textsf{ and }3234?
Is 294 a factor of both 1470 and 3234?
a
Yes
b
No
4
A LaTex expression showing \begin{align*}525 &= 3 times 5 to the power of 2 times 7\\[-0.5em]3850 &= 2 times 5 to the power of 2 times 7 times 11\\[-0.5em]4550 &= 2 times 5 to the power of 2 times 7 times 13\end{align*}\\\\ \textsf{is }525\textsf{ a factor of}\\3850\textsf{ and }4550?
Is 525 a factor of both 3850 and 4550?
a
Yes
b
No
5
A LaTex expression showing \begin{align*}225 &= 3 to the power of 2 times 5 to the power of 2 \\[-0.5em]450 &= 2 times 3 to the power of 2 times 5 to the power of 2 \\[-0.5em]1575 &= 3 to the power of 2 times 5 to the power of 2 times 7\end{align*}\\\\ \textsf{is }225\textsf{ a factor of}\\450\textsf{ and }1575?
Is 225 a factor of both 450 and 1575?
a
Yes
b
No
6
A LaTex expression showing \begin{align*}84 &= 2 to the power of 2 times 3 times 7\\[-0.5em]2310 &= 2 times 3 times 5 times 7 times 11\\[-0.5em]2730 &= 2 times 3 times 5 times 7 times 13\end{align*}\\\\ \textsf{is }84\textsf{ a factor of}\\2310\textsf{ and }2730?
Is 84 a factor of both 2310 and 2730?
a
Yes
b
No
7
A LaTex expression showing \begin{align*}56 &= 2 to the power of 3 times 7\\[-0.5em]168 &= 2 to the power of 3 times 3 times 7\\[-0.5em]280 &= 2 to the power of 3 times 5 times 7\end{align*}\\\\ \textsf{is }56\textsf{ a factor of}\\168\textsf{ and }280?
Is 56 a factor of both 168 and 280?
a
Yes
b
No