HomePricing
Sign InJoin

Prime Factorization - Is Integer a Factor of Both - From Values as Factors (Level 2)

This math topic focuses on prime factorization and explores whether specific integers are common factors of two given numbers. Each question presents the prime factorization of certain numbers and asks if a listed integer is a factor of both provided numbers. The integers and numbers are given in algebraic form, and the exercise helps strengthen understanding of factors, prime factorization, and the greatest common factor. This set of problems is suitable for those practicing factoring skills, specifically in identifying shared factors between numbers.

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

View Unit

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 105 a factor of both 330 and 910?

105=b⋅n⋅p330=2⋅3⋅5⋅11910=2⋅5⋅7⋅13is 105 a factor of330 and 910?\begin{align*}105 &= b \cdot n \cdot p\\[-0.5em]330 &= 2 \cdot 3 \cdot 5 \cdot 11\\[-0.5em]910 &= 2 \cdot 5 \cdot 7 \cdot 13\end{align*}\\\\ \textsf{is }105\textsf{ a factor of}\\330\textsf{ and }910?

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

Mobius Math Club logo
Math worksheet on 'Prime Factorization - Is Integer a Factor of Both - From Values as Factors (Level 2)'. Part of a broader unit on 'Digits and Divisibility - Intro' Learn online: app.mobius.academy/math/units/digits_and_divisibility_intro/
1
A LaTex expression showing \begin{align*}125 &= x to the power of 3 \\[-0.5em]250 &= 2 times 5 to the power of 3 \\[-0.5em]375 &= 3 times 5 to the power of 3 \end{align*}\\\\ \textsf{is }125\textsf{ a factor of}\\250\textsf{ and }375?
Is 125 a factor of both 250 and 375?
a
Yes
b
No
2
A LaTex expression showing \begin{align*}12 &= m to the power of 2 times b\\[-0.5em]210 &= 2 times 3 times 5 times 7\\[-0.5em]220 &= 2 to the power of 2 times 5 times 11\end{align*}\\\\ \textsf{is }12\textsf{ a factor of}\\210\textsf{ and }220?
Is 12 a factor of both 210 and 220?
a
Yes
b
No
3
A LaTex expression showing \begin{align*}45 &= x to the power of 2 times p\\[-0.5em]126 &= 2 times 3 to the power of 2 times 7\\[-0.5em]330 &= 2 times 3 times 5 times 11\end{align*}\\\\ \textsf{is }45\textsf{ a factor of}\\126\textsf{ and }330?
Is 45 a factor of both 126 and 330?
a
Yes
b
No
4
A LaTex expression showing \begin{align*}50 &= c times d to the power of 2 \\[-0.5em]150 &= 2 times 3 times 5 to the power of 2 \\[-0.5em]350 &= 2 times 5 to the power of 2 times 7\end{align*}\\\\ \textsf{is }50\textsf{ a factor of}\\150\textsf{ and }350?
Is 50 a factor of both 150 and 350?
a
Yes
b
No
5
A LaTex expression showing \begin{align*}12 &= z to the power of 2 times n\\[-0.5em]140 &= 2 to the power of 2 times 5 times 7\\[-0.5em]330 &= 2 times 3 times 5 times 11\end{align*}\\\\ \textsf{is }12\textsf{ a factor of}\\140\textsf{ and }330?
Is 12 a factor of both 140 and 330?
a
Yes
b
No
6
A LaTex expression showing \begin{align*}245 &= m times p to the power of 2 \\[-0.5em]294 &= 2 times 3 times 7 to the power of 2 \\[-0.5em]770 &= 2 times 5 times 7 times 11\end{align*}\\\\ \textsf{is }245\textsf{ a factor of}\\294\textsf{ and }770?
Is 245 a factor of both 294 and 770?
a
Yes
b
No
7
A LaTex expression showing \begin{align*}45 &= x to the power of 2 times p\\[-0.5em]210 &= 2 times 3 times 5 times 7\\[-0.5em]330 &= 2 times 3 times 5 times 11\end{align*}\\\\ \textsf{is }45\textsf{ a factor of}\\210\textsf{ and }330?
Is 45 a factor of both 210 and 330?
a
Yes
b
No