Prime Factorizatio

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 315 a factor of both 1386 and 2730?

\begin{align*}315 &= 3^2 \cdot 5 \cdot 7\\\\[-0.5em]1386 &= 2 \cdot 3^2 \cdot 7 \cdot 11\\[-0.5em]2730 &= 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13\end{align*}\\\\ \textsf{is }315\textsf{ a factor of}\\1386\textsf{ and }2730?

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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 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/

$A LaTex expression showing \begin{align*}1225 &= 5 to the power of 2 times 7 to the power of 2 \\\\[-0.5em]2450 &= 2 times 5 to the power of 2 times 7 to the power of 2 \\[-0.5em]3675 &= 3 times 5 to the power of 2 times 7 to the power of 2 \end{align*}\\\\ \textsf{is }1225\textsf{ a factor of}\\2450\textsf{ and }3675?$

Is 1225 a factor of both 2450 and 3675?

Yes

$A LaTex expression showing \begin{align*}1715 &= 5 times 7 to the power of 3 \\\\[-0.5em]3430 &= 2 times 5 times 7 to the power of 3 \\[-0.5em]5145 &= 3 times 5 times 7 to the power of 3 \end{align*}\\\\ \textsf{is }1715\textsf{ a factor of}\\3430\textsf{ and }5145?$

Is 1715 a factor of both 3430 and 5145?

Yes

$A LaTex expression showing \begin{align*}150 &= 2 times 3 times 5 to the power of 2 \\\\[-0.5em]1050 &= 2 times 3 times 5 to the power of 2 times 7\\[-0.5em]1650 &= 2 times 3 times 5 to the power of 2 times 11\end{align*}\\\\ \textsf{is }150\textsf{ a factor of}\\1050\textsf{ and }1650?$

Is 150 a factor of both 1050 and 1650?

Yes

$A LaTex expression showing \begin{align*}735 &= 3 times 5 times 7 to the power of 2 \\\\[-0.5em]2310 &= 2 times 3 times 5 times 7 times 11\\[-0.5em]3822 &= 2 times 3 times 7 to the power of 2 times 13\end{align*}\\\\ \textsf{is }735\textsf{ a factor of}\\2310\textsf{ and }3822?$

Is 735 a factor of both 2310 and 3822?

Yes

$A LaTex expression showing \begin{align*}525 &= 3 times 5 to the power of 2 times 7\\\\[-0.5em]2310 &= 2 times 3 times 5 times 7 times 11\\[-0.5em]1950 &= 2 times 3 times 5 to the power of 2 times 13\end{align*}\\\\ \textsf{is }525\textsf{ a factor of}\\2310\textsf{ and }1950?$

Is 525 a factor of both 2310 and 1950?

Yes

$A LaTex expression showing \begin{align*}294 &= 2 times 3 times 7 to the power of 2 \\\\[-0.5em]5390 &= 2 times 5 times 7 to the power of 2 times 11\\[-0.5em]2730 &= 2 times 3 times 5 times 7 times 13\end{align*}\\\\ \textsf{is }294\textsf{ a factor of}\\5390\textsf{ and }2730?$

Is 294 a factor of both 5390 and 2730?

Yes

$A LaTex expression showing \begin{align*}294 &= 2 times 3 times 7 to the power of 2 \\\\[-0.5em]8085 &= 3 times 5 times 7 to the power of 2 times 11\\[-0.5em]9555 &= 3 times 5 times 7 to the power of 2 times 13\end{align*}\\\\ \textsf{is }294\textsf{ a factor of}\\8085\textsf{ and }9555?$

Is 294 a factor of both 8085 and 9555?

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