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

This math topic focuses on practicing prime factorization for determining whether a given number is a common factor of two other numbers. Each problem presents the prime factors of three numbers and asks if one of these is a factor of the other two. This is aimed at developing skills in factoring numbers and understanding the greatest common factor, which are fundamental concepts in arithmetic and number theory. The problems require students to analyze the prime factorization for common factors and deduce divisibility, aiding in the comprehension of factor relationships and multiplication.

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

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Is Number 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 4 a factor of both 12 and 20?

4=2212=22⋅320=22⋅5is 4 a factor of12 and 20?\begin{align*}4 &= 2^2\\[-0.5em]12 &= 2^2 \cdot 3\\[-0.5em]20 &= 2^2 \cdot 5\end{align*}\\\\ \textsf{is }4\textsf{ a factor of}\\12\textsf{ and }20?

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

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Math worksheet on 'Prime Factorization - Is Number 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*}10 &= 2 times 5\\[-0.5em]42 &= 2 times 3 times 7\\[-0.5em]66 &= 2 times 3 times 11\end{align*}\\\\ \textsf{is }10\textsf{ a factor of}\\42\textsf{ and }66?
Is 10 a factor of both 42 and 66?
a
Yes
b
No
2
A LaTex expression showing \begin{align*}10 &= 2 times 5\\[-0.5em]105 &= 3 times 5 times 7\\[-0.5em]66 &= 2 times 3 times 11\end{align*}\\\\ \textsf{is }10\textsf{ a factor of}\\105\textsf{ and }66?
Is 10 a factor of both 105 and 66?
a
Yes
b
No
3
A LaTex expression showing \begin{align*}9 &= 3 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
4
A LaTex expression showing \begin{align*}4 &= 2 to the power of 2 \\[-0.5em]12 &= 2 to the power of 2 times 3\\[-0.5em]20 &= 2 to the power of 2 times 5\end{align*}\\\\ \textsf{is }4\textsf{ a factor of}\\12\textsf{ and }20?
Is 4 a factor of both 12 and 20?
a
Yes
b
No
5
A LaTex expression showing \begin{align*}14 &= 2 times 7\\[-0.5em]42 &= 2 times 3 times 7\\[-0.5em]70 &= 2 times 5 times 7\end{align*}\\\\ \textsf{is }14\textsf{ a factor of}\\42\textsf{ and }70?
Is 14 a factor of both 42 and 70?
a
Yes
b
No
6
A LaTex expression showing \begin{align*}6 &= 2 times 3\\[-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
7
A LaTex expression showing \begin{align*}6 &= 2 times 3\\[-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