Prime Factorizatio

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 30 and 42?

\begin{align*}4 &= 2^2\\\\[-0.5em]30 &= 2 \cdot 3 \cdot 5\\[-0.5em]42 &= 2 \cdot 3 \cdot 7\end{align*}\\\\ \textsf{is }4\textsf{ a factor of}\\30\textsf{ and }42?

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

Math worksheet on 'Prime Factorization - Is Number a Factor of Both - From Values as Factors (Level 1)'. Part of a broader unit on 'Factoring and Venn Factor Diagrams - Practice' Learn online: app.mobius.academy/math/units/factoring_and_venn_diagrams_practice/

$A LaTex expression showing \begin{align*}14 &= 2 times 7\\\\[-0.5em]105 &= 3 times 5 times 7\\[-0.5em]66 &= 2 times 3 times 11\end{align*}\\\\ \textsf{is }14\textsf{ a factor of}\\105\textsf{ and }66?$

Is 14 a factor of both 105 and 66?

Yes

$A LaTex expression showing \begin{align*}21 &= 3 times 7\\\\[-0.5em]70 &= 2 times 5 times 7\\[-0.5em]154 &= 2 times 7 times 11\end{align*}\\\\ \textsf{is }21\textsf{ a factor of}\\70\textsf{ and }154?$

Is 21 a factor of both 70 and 154?

Yes

$A LaTex expression showing \begin{align*}15 &= 3 times 5\\\\[-0.5em]70 &= 2 times 5 times 7\\[-0.5em]110 &= 2 times 5 times 11\end{align*}\\\\ \textsf{is }15\textsf{ a factor of}\\70\textsf{ and }110?$

Is 15 a factor of both 70 and 110?

Yes

$A LaTex expression showing \begin{align*}10 &= 2 times 5\\\\[-0.5em]105 &= 3 times 5 times 7\\[-0.5em]66 &= 2 times 3 times 11\end{align*}\\\\ \textsf{is }10\textsf{ a factor of}\\105\textsf{ and }66?$

Is 10 a factor of both 105 and 66?

Yes

$A LaTex expression showing \begin{align*}14 &= 2 times 7\\\\[-0.5em]42 &= 2 times 3 times 7\\[-0.5em]70 &= 2 times 5 times 7\end{align*}\\\\ \textsf{is }14\textsf{ a factor of}\\42\textsf{ and }70?$

Is 14 a factor of both 42 and 70?

Yes

$A LaTex expression showing \begin{align*}21 &= 3 times 7\\\\[-0.5em]42 &= 2 times 3 times 7\\[-0.5em]105 &= 3 times 5 times 7\end{align*}\\\\ \textsf{is }21\textsf{ a factor of}\\42\textsf{ and }105?$

Is 21 a factor of both 42 and 105?

Yes

$A LaTex expression showing \begin{align*}6 &= 2 times 3\\\\[-0.5em]30 &= 2 times 3 times 5\\[-0.5em]42 &= 2 times 3 times 7\end{align*}\\\\ \textsf{is }6\textsf{ a factor of}\\30\textsf{ and }42?$

Is 6 a factor of both 30 and 42?

Yes

Prime Factorizatio

Practice:

Is Number a Factor of Both - From Values as Factors

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