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.

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Is Integer a Factor of Both - From Values as Factors

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Is 98 a factor of both 294 and 490?

\begin{align*}98 &= c \cdot x^2\\\\[-0.5em]294 &= 2 \cdot 3 \cdot 7^2\\[-0.5em]490 &= 2 \cdot 5 \cdot 7^2\end{align*}\\\\ \textsf{is }98\textsf{ a factor of}\\294\textsf{ and }490?

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 2)'. 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/

$A LaTex expression showing \begin{align*}175 &= c to the power of 2 times m\\\\[-0.5em]350 &= 2 times 5 to the power of 2 times 7\\[-0.5em]525 &= 3 times 5 to the power of 2 times 7\end{align*}\\\\ \textsf{is }175\textsf{ a factor of}\\350\textsf{ and }525?$

Is 175 a factor of both 350 and 525?

Yes

$A LaTex expression showing \begin{align*}30 &= x times n times y\\\\[-0.5em]770 &= 2 times 5 times 7 times 11\\[-0.5em]910 &= 2 times 5 times 7 times 13\end{align*}\\\\ \textsf{is }30\textsf{ a factor of}\\770\textsf{ and }910?$

Is 30 a factor of both 770 and 910?

Yes

$A LaTex expression showing \begin{align*}30 &= p times z times x\\\\[-0.5em]770 &= 2 times 5 times 7 times 11\\[-0.5em]1365 &= 3 times 5 times 7 times 13\end{align*}\\\\ \textsf{is }30\textsf{ a factor of}\\770\textsf{ and }1365?$

Is 30 a factor of both 770 and 1365?

Yes

$A LaTex expression showing \begin{align*}50 &= y times p to the power of 2 \\\\[-0.5em]210 &= 2 times 3 times 5 times 7\\[-0.5em]825 &= 3 times 5 to the power of 2 times 11\end{align*}\\\\ \textsf{is }50\textsf{ a factor of}\\210\textsf{ and }825?$

Is 50 a factor of both 210 and 825?

Yes

$A LaTex expression showing \begin{align*}70 &= n times d times c\\\\[-0.5em]462 &= 2 times 3 times 7 times 11\\[-0.5em]390 &= 2 times 3 times 5 times 13\end{align*}\\\\ \textsf{is }70\textsf{ a factor of}\\462\textsf{ and }390?$

Is 70 a factor of both 462 and 390?

Yes

$A LaTex expression showing \begin{align*}245 &= p times d to the power of 2 \\\\[-0.5em]490 &= 2 times 5 times 7 to the power of 2 \\[-0.5em]735 &= 3 times 5 times 7 to the power of 2 \end{align*}\\\\ \textsf{is }245\textsf{ a factor of}\\490\textsf{ and }735?$

Is 245 a factor of both 490 and 735?

Yes

$A LaTex expression showing \begin{align*}147 &= d times r to the power of 2 \\\\[-0.5em]294 &= 2 times 3 times 7 to the power of 2 \\[-0.5em]735 &= 3 times 5 times 7 to the power of 2 \end{align*}\\\\ \textsf{is }147\textsf{ a factor of}\\294\textsf{ and }735?$

Is 147 a factor of both 294 and 735?

Yes

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

Practice:

Is Integer a Factor of Both - From Values as Factors

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