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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 686 a factor of both 2058 and 3430?

686=y⋅p32058=2⋅3⋅733430=2⋅5⋅73is 686 a factor of2058 and 3430?\begin{align*}686 &= y \cdot p^3\\[-0.5em]2058 &= 2 \cdot 3 \cdot 7^3\\[-0.5em]3430 &= 2 \cdot 5 \cdot 7^3\end{align*}\\\\ \textsf{is }686\textsf{ a factor of}\\2058\textsf{ and }3430?

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*}210 &= y times n times b times m\\[-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 }210\textsf{ a factor of}\\2310\textsf{ and }2730?
Is 210 a factor of both 2310 and 2730?
a
Yes
b
No
2
A LaTex expression showing \begin{align*}100 &= p to the power of 2 times b to the power of 2 \\[-0.5em]300 &= 2 to the power of 2 times 3 times 5 to the power of 2 \\[-0.5em]700 &= 2 to the power of 2 times 5 to the power of 2 times 7\end{align*}\\\\ \textsf{is }100\textsf{ a factor of}\\300\textsf{ and }700?
Is 100 a factor of both 300 and 700?
a
Yes
b
No
3
A LaTex expression showing \begin{align*}135 &= b to the power of 3 times z\\[-0.5em]378 &= 2 times 3 to the power of 3 times 7\\[-0.5em]990 &= 2 times 3 to the power of 2 times 5 times 11\end{align*}\\\\ \textsf{is }135\textsf{ a factor of}\\378\textsf{ and }990?
Is 135 a factor of both 378 and 990?
a
Yes
b
No
4
A LaTex expression showing \begin{align*}490 &= z times p times n 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
5
A LaTex expression showing \begin{align*}441 &= c to the power of 2 times m to the power of 2 \\[-0.5em]630 &= 2 times 3 to the power of 2 times 5 times 7\\[-0.5em]1386 &= 2 times 3 to the power of 2 times 7 times 11\end{align*}\\\\ \textsf{is }441\textsf{ a factor of}\\630\textsf{ and }1386?
Is 441 a factor of both 630 and 1386?
a
Yes
b
No
6
A LaTex expression showing \begin{align*}140 &= z to the power of 2 times b times r\\[-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
7
A LaTex expression showing \begin{align*}686 &= y times p to the power of 3 \\[-0.5em]2058 &= 2 times 3 times 7 to the power of 3 \\[-0.5em]3430 &= 2 times 5 times 7 to the power of 3 \end{align*}\\\\ \textsf{is }686\textsf{ a factor of}\\2058\textsf{ and }3430?
Is 686 a factor of both 2058 and 3430?
a
Yes
b
No