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

This math topic focuses on advanced factoring skills and the determination of common factors in different numbers. It employs prime factorization to assess whether a given integer is a factor of two other numbers. Problems present equations involving exponentiation and multiplication of prime numbers, requiring students to decide if one number is a factor of the others listed. Each question is structured with two potential answers: "Yes" or "No." This analysis aids students in understanding factor relationships and the concept of the greatest common factor at a deeper level.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Is Integer 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 2310 and 2730?

210=p⋅n⋅r⋅x2310=2⋅3⋅5⋅7⋅112730=2⋅3⋅5⋅7⋅13is 210 a factor of2310 and 2730?\begin{align*}210 &= p \cdot n \cdot r \cdot x\\\\[-0.5em]2310 &= 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11\\[-0.5em]2730 &= 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13\end{align*}\\\\ \textsf{is }210\textsf{ a factor of}\\2310\textsf{ and }2730?

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

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Math worksheet on 'Prime Factorization - Is Integer 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*}490 &= c times d times z to the power of 2 \\\\[-0.5em]3234 &= 2 times 3 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 }490\textsf{ a factor of}\\3234\textsf{ and }2730?
Is 490 a factor of both 3234 and 2730?
a
Yes
b
No
2
A LaTex expression showing \begin{align*}90 &= d times n to the power of 2 times m\\\\[-0.5em]630 &= 2 times 3 to the power of 2 times 5 times 7\\[-0.5em]990 &= 2 times 3 to the power of 2 times 5 times 11\end{align*}\\\\ \textsf{is }90\textsf{ a factor of}\\630\textsf{ and }990?
Is 90 a factor of both 630 and 990?
a
Yes
b
No
3
A LaTex expression showing \begin{align*}315 &= r to the power of 2 times p times z\\\\[-0.5em]630 &= 2 times 3 to the power of 2 times 5 times 7\\[-0.5em]3465 &= 3 to the power of 2 times 5 times 7 times 11\end{align*}\\\\ \textsf{is }315\textsf{ a factor of}\\630\textsf{ and }3465?
Is 315 a factor of both 630 and 3465?
a
Yes
b
No
4
A LaTex expression showing \begin{align*}225 &= n to the power of 2 times b to the power of 2 \\\\[-0.5em]630 &= 2 times 3 to the power of 2 times 5 times 7\\[-0.5em]1650 &= 2 times 3 times 5 to the power of 2 times 11\end{align*}\\\\ \textsf{is }225\textsf{ a factor of}\\630\textsf{ and }1650?
Is 225 a factor of both 630 and 1650?
a
Yes
b
No
5
A LaTex expression showing \begin{align*}126 &= d times y to the power of 2 times b\\\\[-0.5em]2310 &= 2 times 3 times 5 times 7 times 11\\[-0.5em]4095 &= 3 to the power of 2 times 5 times 7 times 13\end{align*}\\\\ \textsf{is }126\textsf{ a factor of}\\2310\textsf{ and }4095?
Is 126 a factor of both 2310 and 4095?
a
Yes
b
No
6
A LaTex expression showing \begin{align*}84 &= y to the power of 2 times p times x\\\\[-0.5em]420 &= 2 to the power of 2 times 3 times 5 times 7\\[-0.5em]924 &= 2 to the power of 2 times 3 times 7 times 11\end{align*}\\\\ \textsf{is }84\textsf{ a factor of}\\420\textsf{ and }924?
Is 84 a factor of both 420 and 924?
a
Yes
b
No
7
A LaTex expression showing \begin{align*}40 &= p to the power of 3 times d\\\\[-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