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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 140 a factor of both 420 and 1540?

140=22⋅5⋅7420=22⋅3⋅5⋅71540=22⋅5⋅7⋅11is 140 a factor of420 and 1540?\begin{align*}140 &= 2^2 \cdot 5 \cdot 7\\\\[-0.5em]420 &= 2^2 \cdot 3 \cdot 5 \cdot 7\\[-0.5em]1540 &= 2^2 \cdot 5 \cdot 7 \cdot 11\end{align*}\\\\ \textsf{is }140\textsf{ a factor of}\\420\textsf{ and }1540?

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 - Intro' Learn online: app.mobius.academy/math/units/factoring_and_greatest_common_factor_intro/
1
A LaTex expression showing \begin{align*}1225 &= 5 to the power of 2 times 7 to the power of 2 \\\\[-0.5em]2450 &= 2 times 5 to the power of 2 times 7 to the power of 2 \\[-0.5em]3675 &= 3 times 5 to the power of 2 times 7 to the power of 2 \end{align*}\\\\ \textsf{is }1225\textsf{ a factor of}\\2450\textsf{ and }3675?
Is 1225 a factor of both 2450 and 3675?
a
Yes
b
No
2
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
3
A LaTex expression showing \begin{align*}150 &= 2 times 3 times 5 to the power of 2 \\\\[-0.5em]1050 &= 2 times 3 times 5 to the power of 2 times 7\\[-0.5em]1650 &= 2 times 3 times 5 to the power of 2 times 11\end{align*}\\\\ \textsf{is }150\textsf{ a factor of}\\1050\textsf{ and }1650?
Is 150 a factor of both 1050 and 1650?
a
Yes
b
No
4
A LaTex expression showing \begin{align*}735 &= 3 times 5 times 7 to the power of 2 \\\\[-0.5em]2310 &= 2 times 3 times 5 times 7 times 11\\[-0.5em]3822 &= 2 times 3 times 7 to the power of 2 times 13\end{align*}\\\\ \textsf{is }735\textsf{ a factor of}\\2310\textsf{ and }3822?
Is 735 a factor of both 2310 and 3822?
a
Yes
b
No
5
A LaTex expression showing \begin{align*}525 &= 3 times 5 to the power of 2 times 7\\\\[-0.5em]2310 &= 2 times 3 times 5 times 7 times 11\\[-0.5em]1950 &= 2 times 3 times 5 to the power of 2 times 13\end{align*}\\\\ \textsf{is }525\textsf{ a factor of}\\2310\textsf{ and }1950?
Is 525 a factor of both 2310 and 1950?
a
Yes
b
No
6
A LaTex expression showing \begin{align*}294 &= 2 times 3 times 7 to the power of 2 \\\\[-0.5em]5390 &= 2 times 5 times 7 to the power of 2 times 11\\[-0.5em]2730 &= 2 times 3 times 5 times 7 times 13\end{align*}\\\\ \textsf{is }294\textsf{ a factor of}\\5390\textsf{ and }2730?
Is 294 a factor of both 5390 and 2730?
a
Yes
b
No
7
A LaTex expression showing \begin{align*}294 &= 2 times 3 times 7 to the power of 2 \\\\[-0.5em]8085 &= 3 times 5 times 7 to the power of 2 times 11\\[-0.5em]9555 &= 3 times 5 times 7 to the power of 2 times 13\end{align*}\\\\ \textsf{is }294\textsf{ a factor of}\\8085\textsf{ and }9555?
Is 294 a factor of both 8085 and 9555?
a
Yes
b
No