Prime Factorization - Is Number a Factor of Both - From Variables as Factors (Level 2)

This math topic focuses on evaluating the divisibility of numbers by examining prime factorization. It combines the concepts of factoring and finding the greatest common factor (GCF) in practical scenarios. Each question lists two expressions involving products of prime factors and asks whether one expression is a factor of the other two given expressions. The problems help enhance understanding of prime factorization, examining common factors, and applying these skills in finding whether one number is a factor of others. This is essential for developing skills in higher mathematics, particularly in algebra and number theory.

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Is Number a Factor of Both - From Variables as Factors

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Is m a factor of both 210 and 330?

\begin{align*}m &= 2^2 \cdot 3\\\\[-0.5em]210 &= 2 \cdot 3 \cdot 5 \cdot 7\\[-0.5em]330 &= 2 \cdot 3 \cdot 5 \cdot 11\end{align*}\\\\ \textsf{is }m\textsf{ a factor of}\\210\textsf{ and }330?

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

Math worksheet on 'Prime Factorization - Is Number a Factor of Both - From Variables 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/

$A LaTex expression showing \begin{align*}m &= 3 to the power of 2 times 7\\\\[-0.5em]126 &= 2 times 3 to the power of 2 times 7\\[-0.5em]315 &= 3 to the power of 2 times 5 times 7\end{align*}\\\\ \textsf{is }m\textsf{ a factor of}\\126\textsf{ and }315?$

Is m a factor of both 126 and 315?

Yes

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

Is d a factor of both 490 and 735?

Yes

$A LaTex expression showing \begin{align*}b &= 2 times 5 times 7\\\\[-0.5em]210 &= 2 times 3 times 5 times 7\\[-0.5em]770 &= 2 times 5 times 7 times 11\end{align*}\\\\ \textsf{is }b\textsf{ a factor of}\\210\textsf{ and }770?$

Is b a factor of both 210 and 770?

Yes

$A LaTex expression showing \begin{align*}y &= 3 to the power of 2 times 7\\\\[-0.5em]126 &= 2 times 3 to the power of 2 times 7\\[-0.5em]315 &= 3 to the power of 2 times 5 times 7\end{align*}\\\\ \textsf{is }y\textsf{ a factor of}\\126\textsf{ and }315?$

Is y a factor of both 126 and 315?

Yes

$A LaTex expression showing \begin{align*}z &= 2 times 5 to the power of 2 \\\\[-0.5em]150 &= 2 times 3 times 5 to the power of 2 \\[-0.5em]350 &= 2 times 5 to the power of 2 times 7\end{align*}\\\\ \textsf{is }z\textsf{ a factor of}\\150\textsf{ and }350?$

Is z a factor of both 150 and 350?

Yes

$A LaTex expression showing \begin{align*}y &= 2 times 3 times 5\\\\[-0.5em]462 &= 2 times 3 times 7 times 11\\[-0.5em]910 &= 2 times 5 times 7 times 13\end{align*}\\\\ \textsf{is }y\textsf{ a factor of}\\462\textsf{ and }910?$

Is y a factor of both 462 and 910?

Yes

$A LaTex expression showing \begin{align*}b &= 2 times 5 to the power of 2 \\\\[-0.5em]150 &= 2 times 3 times 5 to the power of 2 \\[-0.5em]350 &= 2 times 5 to the power of 2 times 7\end{align*}\\\\ \textsf{is }b\textsf{ a factor of}\\150\textsf{ and }350?$

Is b a factor of both 150 and 350?

Yes

Prime Factorization - Is Number a Factor of Both - From Variables as Factors (Level 2)

Practice:

Is Number a Factor of Both - From Variables as Factors

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