Prime Factorization - Is Number a Multiple of Both - From Variables as Factors (Level 3)

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

$A LaTex expression showing \begin{align*}b &= 3 times 5 times 7 to the power of 3 \\\\[-0.5em]735 &= 3 times 5 times 7 to the power of 2 \\[-0.5em]1029 &= 3 times 7 to the power of 3 \end{align*}\\\\ \textsf{is }b\textsf{ a multiple of }\\735\textsf{ and }1029?$

Is b a multiple of both 735 and 1029?

Yes

$A LaTex expression showing \begin{align*}z &= 2 to the power of 2 times 3 times 7 to the power of 2 \\\\[-0.5em]84 &= 2 to the power of 2 times 3 times 7\\[-0.5em]294 &= 2 times 3 times 7 to the power of 2 \end{align*}\\\\ \textsf{is }z\textsf{ a multiple of }\\84\textsf{ and }294?$

Is z a multiple of both 84 and 294?

Yes

$A LaTex expression showing \begin{align*}n &= 2 to the power of 3 times 5 times 7\\\\[-0.5em]140 &= 2 to the power of 2 times 5 times 7\\[-0.5em]40 &= 2 to the power of 3 times 5\end{align*}\\\\ \textsf{is }n\textsf{ a multiple of }\\140\textsf{ and }40?$

Is n a multiple of both 140 and 40?

Yes

$A LaTex expression showing \begin{align*}n &= 2 to the power of 2 times 5 to the power of 3 \\\\[-0.5em]60 &= 2 to the power of 2 times 3 times 5\\[-0.5em]250 &= 2 times 5 to the power of 3 \end{align*}\\\\ \textsf{is }n\textsf{ a multiple of }\\60\textsf{ and }250?$

Is n a multiple of both 60 and 250?

Yes

$A LaTex expression showing \begin{align*}x &= 3 to the power of 3 times 5 times 7\\\\[-0.5em]459 &= 3 to the power of 3 times 17\\[-0.5em]315 &= 3 to the power of 2 times 5 times 7\end{align*}\\\\ \textsf{is }x\textsf{ a multiple of }\\459\textsf{ and }315?$

Is x a multiple of both 459 and 315?

Yes

$A LaTex expression showing \begin{align*}p &= 2 times 3 to the power of 3 times 7\\\\[-0.5em]90 &= 2 times 3 to the power of 2 times 5\\[-0.5em]126 &= 2 times 3 to the power of 2 times 7\end{align*}\\\\ \textsf{is }p\textsf{ a multiple of }\\90\textsf{ and }126?$

Is p a multiple of both 90 and 126?

Yes

$A LaTex expression showing \begin{align*}z &= 3 times 5 to the power of 2 times 7 to the power of 2 \\\\[-0.5em]1225 &= 5 to the power of 2 times 7 to the power of 2 \\[-0.5em]735 &= 3 times 5 times 7 to the power of 2 \end{align*}\\\\ \textsf{is }z\textsf{ a multiple of }\\1225\textsf{ and }735?$

Is z a multiple of both 1225 and 735?

Yes

$A LaTex expression showing \begin{align*}z &= 2 times 3 times 5 to the power of 2 times 7\\\\[-0.5em]330 &= 2 times 3 times 5 times 11\\[-0.5em]150 &= 2 times 3 times 5 to the power of 2 \end{align*}\\\\ \textsf{is }z\textsf{ a multiple of }\\330\textsf{ and }150?$

Is z a multiple of both 330 and 150?

Yes

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