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

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

$A LaTex expression showing \begin{align*}675 &= 3 to the power of 3 times 5 to the power of 2 \\\\[-0.5em]135 &= 3 to the power of 3 times 5\\[-0.5em]225 &= 3 to the power of 2 times 5 to the power of 2 \end{align*}\\\\ \textsf{is }675\textsf{ a multiple of }\\135\textsf{ and }225?$

Is 675 a multiple of both 135 and 225?

Yes

$A LaTex expression showing \begin{align*}420 &= 2 to the power of 2 times 3 times 5 times 7\\\\[-0.5em]84 &= 2 to the power of 2 times 3 times 7\\[-0.5em]210 &= 2 times 3 times 5 times 7\end{align*}\\\\ \textsf{is }420\textsf{ a multiple of }\\84\textsf{ and }210?$

Is 420 a multiple of both 84 and 210?

Yes

$A LaTex expression showing \begin{align*}980 &= 2 to the power of 2 times 5 times 7 to the power of 2 \\\\[-0.5em]220 &= 2 to the power of 2 times 5 times 11\\[-0.5em]490 &= 2 times 5 times 7 to the power of 2 \end{align*}\\\\ \textsf{is }980\textsf{ a multiple of }\\220\textsf{ and }490?$

Is 980 a multiple of both 220 and 490?

Yes

$A LaTex expression showing \begin{align*}3430 &= 2 times 5 times 7 to the power of 3 \\\\[-0.5em]686 &= 2 times 7 to the power of 3 \\[-0.5em]490 &= 2 times 5 times 7 to the power of 2 \end{align*}\\\\ \textsf{is }3430\textsf{ a multiple of }\\686\textsf{ and }490?$

Is 3430 a multiple of both 686 and 490?

Yes

$A LaTex expression showing \begin{align*}270 &= 2 times 3 to the power of 3 times 5\\\\[-0.5em]126 &= 2 times 3 to the power of 2 times 7\\[-0.5em]90 &= 2 times 3 to the power of 2 times 5\end{align*}\\\\ \textsf{is }270\textsf{ a multiple of }\\126\textsf{ and }90?$

Is 270 a multiple of both 126 and 90?

Yes

$A LaTex expression showing \begin{align*}630 &= 2 times 3 to the power of 2 times 5 times 7\\\\[-0.5em]210 &= 2 times 3 times 5 times 7\\[-0.5em]315 &= 3 to the power of 2 times 5 times 7\end{align*}\\\\ \textsf{is }630\textsf{ a multiple of }\\210\textsf{ and }315?$

Is 630 a multiple of both 210 and 315?

Yes

$A LaTex expression showing \begin{align*}1250 &= 2 times 5 to the power of 4 \\\\[-0.5em]250 &= 2 times 5 to the power of 3 \\[-0.5em]625 &= 5 to the power of 4 \end{align*}\\\\ \textsf{is }1250\textsf{ a multiple of }\\250\textsf{ and }625?$

Is 1250 a multiple of both 250 and 625?

Yes

$A LaTex expression showing \begin{align*}700 &= 2 to the power of 2 times 5 to the power of 2 times 7\\\\[-0.5em]140 &= 2 to the power of 2 times 5 times 7\\[-0.5em]350 &= 2 times 5 to the power of 2 times 7\end{align*}\\\\ \textsf{is }700\textsf{ a multiple of }\\140\textsf{ and }350?$

Is 700 a multiple of both 140 and 350?

Yes

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