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

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Prime Factorization - Is Number a Factor of Both - From Values as Factors
1
A LaTex expression showing \begin{align*}90 &= 2 times 3 to the power of 2 times 5\\\\[-0.5em]1386 &= 2 times 3 to the power of 2 times 7 times 11\\[-0.5em]4095 &= 3 to the power of 2 times 5 times 7 times 13\end{align*}\\\\ \textsf{is }90\textsf{ a factor of}\\1386\textsf{ and }4095?
Is 90 a factor of both 1386 and 4095?
a
Yes
b
No
2
A LaTex expression showing \begin{align*}140 &= 2 to the power of 2 times 5 times 7\\\\[-0.5em]420 &= 2 to the power of 2 times 3 times 5 times 7\\[-0.5em]1540 &= 2 to the power of 2 times 5 times 7 times 11\end{align*}\\\\ \textsf{is }140\textsf{ a factor of}\\420\textsf{ and }1540?
Is 140 a factor of both 420 and 1540?
a
Yes
b
No
3
A LaTex expression showing \begin{align*}490 &= 2 times 5 times 7 to the power of 2 \\\\[-0.5em]1470 &= 2 times 3 times 5 times 7 to the power of 2 \\[-0.5em]5390 &= 2 times 5 times 7 to the power of 2 times 11\end{align*}\\\\ \textsf{is }490\textsf{ a factor of}\\1470\textsf{ and }5390?
Is 490 a factor of both 1470 and 5390?
a
Yes
b
No
4
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]9555 &= 3 times 5 times 7 to the power of 2 times 13\end{align*}\\\\ \textsf{is }294\textsf{ a factor of}\\5390\textsf{ and }9555?
Is 294 a factor of both 5390 and 9555?
a
Yes
b
No
5
A LaTex expression showing \begin{align*}490 &= 2 times 5 times 7 to the power of 2 \\\\[-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 }490\textsf{ a factor of}\\2310\textsf{ and }2730?
Is 490 a factor of both 2310 and 2730?
a
Yes
b
No
6
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
7
A LaTex expression showing \begin{align*}735 &= 3 times 5 times 7 to the power of 2 \\\\[-0.5em]1470 &= 2 times 3 times 5 times 7 to the power of 2 \\[-0.5em]8085 &= 3 times 5 times 7 to the power of 2 times 11\end{align*}\\\\ \textsf{is }735\textsf{ a factor of}\\1470\textsf{ and }8085?
Is 735 a factor of both 1470 and 8085?
a
Yes
b
No
8
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