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Prime Factorization - Is Integer a Factor of Both - From Values as Factors (Level 1)

This math topic focuses on the skills of prime factorization and evaluating if one integer is a factor of two other integers. The problems require identifying the factors of given numbers, represented in prime factorization, and determining whether a specific integer, also given in a factored form, is a common factor of both numbers. The exercises are structured to enhance understanding of factoring and the concept of the greatest common factor. Each problem presents two numbers with their prime factors listed and asks whether a given integer is a factor of both.

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

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Is 15 a factor of both 30 and 105?

15=y⋅p30=2⋅3⋅5105=3⋅5⋅7is 15 a factor of30 and 105?\begin{align*}15 &= y \cdot p\\[-0.5em]30 &= 2 \cdot 3 \cdot 5\\[-0.5em]105 &= 3 \cdot 5 \cdot 7\end{align*}\\\\ \textsf{is }15\textsf{ a factor of}\\30\textsf{ and }105?

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 1)'. 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*}35 &= m times d\\[-0.5em]42 &= 2 times 3 times 7\\[-0.5em]110 &= 2 times 5 times 11\end{align*}\\\\ \textsf{is }35\textsf{ a factor of}\\42\textsf{ and }110?
Is 35 a factor of both 42 and 110?
a
Yes
b
No
2
A LaTex expression showing \begin{align*}9 &= n to the power of 2 \\[-0.5em]18 &= 2 times 3 to the power of 2 \\[-0.5em]45 &= 3 to the power of 2 times 5\end{align*}\\\\ \textsf{is }9\textsf{ a factor of}\\18\textsf{ and }45?
Is 9 a factor of both 18 and 45?
a
Yes
b
No
3
A LaTex expression showing \begin{align*}4 &= r to the power of 2 \\[-0.5em]30 &= 2 times 3 times 5\\[-0.5em]42 &= 2 times 3 times 7\end{align*}\\\\ \textsf{is }4\textsf{ a factor of}\\30\textsf{ and }42?
Is 4 a factor of both 30 and 42?
a
Yes
b
No
4
A LaTex expression showing \begin{align*}6 &= r times z\\[-0.5em]105 &= 3 times 5 times 7\\[-0.5em]165 &= 3 times 5 times 11\end{align*}\\\\ \textsf{is }6\textsf{ a factor of}\\105\textsf{ and }165?
Is 6 a factor of both 105 and 165?
a
Yes
b
No
5
A LaTex expression showing \begin{align*}6 &= z times d\\[-0.5em]30 &= 2 times 3 times 5\\[-0.5em]42 &= 2 times 3 times 7\end{align*}\\\\ \textsf{is }6\textsf{ a factor of}\\30\textsf{ and }42?
Is 6 a factor of both 30 and 42?
a
Yes
b
No
6
A LaTex expression showing \begin{align*}21 &= c times r\\[-0.5em]42 &= 2 times 3 times 7\\[-0.5em]105 &= 3 times 5 times 7\end{align*}\\\\ \textsf{is }21\textsf{ a factor of}\\42\textsf{ and }105?
Is 21 a factor of both 42 and 105?
a
Yes
b
No
7
A LaTex expression showing \begin{align*}21 &= b times p\\[-0.5em]30 &= 2 times 3 times 5\\[-0.5em]66 &= 2 times 3 times 11\end{align*}\\\\ \textsf{is }21\textsf{ a factor of}\\30\textsf{ and }66?
Is 21 a factor of both 30 and 66?
a
Yes
b
No