Prime Factorizatio

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?

\begin{align*}15 &= z \cdot x\\\\[-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?

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

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

$A LaTex expression showing \begin{align*}6 &= p times m\\\\[-0.5em]105 &= 3 times 5 times 7\\[-0.5em]110 &= 2 times 5 times 11\end{align*}\\\\ \textsf{is }6\textsf{ a factor of}\\105\textsf{ and }110?$

Is 6 a factor of both 105 and 110?

Yes

$A LaTex expression showing \begin{align*}9 &= x to the power of 2 \\\\[-0.5em]30 &= 2 times 3 times 5\\[-0.5em]42 &= 2 times 3 times 7\end{align*}\\\\ \textsf{is }9\textsf{ a factor of}\\30\textsf{ and }42?$

Is 9 a factor of both 30 and 42?

Yes

$A LaTex expression showing \begin{align*}15 &= p times y\\\\[-0.5em]70 &= 2 times 5 times 7\\[-0.5em]66 &= 2 times 3 times 11\end{align*}\\\\ \textsf{is }15\textsf{ a factor of}\\70\textsf{ and }66?$

Is 15 a factor of both 70 and 66?

Yes

$A LaTex expression showing \begin{align*}35 &= m times b\\\\[-0.5em]70 &= 2 times 5 times 7\\[-0.5em]105 &= 3 times 5 times 7\end{align*}\\\\ \textsf{is }35\textsf{ a factor of}\\70\textsf{ and }105?$

Is 35 a factor of both 70 and 105?

Yes

$A LaTex expression showing \begin{align*}14 &= r times n\\\\[-0.5em]105 &= 3 times 5 times 7\\[-0.5em]231 &= 3 times 7 times 11\end{align*}\\\\ \textsf{is }14\textsf{ a factor of}\\105\textsf{ and }231?$

Is 14 a factor of both 105 and 231?

Yes

$A LaTex expression showing \begin{align*}25 &= y to the power of 2 \\\\[-0.5em]50 &= 2 times 5 to the power of 2 \\[-0.5em]75 &= 3 times 5 to the power of 2 \end{align*}\\\\ \textsf{is }25\textsf{ a factor of}\\50\textsf{ and }75?$

Is 25 a factor of both 50 and 75?

Yes

$A LaTex expression showing \begin{align*}21 &= c times r\\\\[-0.5em]70 &= 2 times 5 times 7\\[-0.5em]66 &= 2 times 3 times 11\end{align*}\\\\ \textsf{is }21\textsf{ a factor of}\\70\textsf{ and }66?$

Is 21 a factor of both 70 and 66?

Yes

Prime Factorizatio

Practice:

Is Integer a Factor of Both - From Values as Factors

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