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

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

$A LaTex expression showing \begin{align*}y &= 2 to the power of 3 times 3\\\\[-0.5em]12 &= 2 to the power of 2 times 3\\[-0.5em]8 &= 2 to the power of 3 \end{align*}\\\\ \textsf{is }y\textsf{ a multiple of }\\12\textsf{ and }8?$

Is y a multiple of both 12 and 8?

Yes

$A LaTex expression showing \begin{align*}y &= 2 to the power of 2 times 3 times 7\\\\[-0.5em]20 &= 2 to the power of 2 times 5\\[-0.5em]28 &= 2 to the power of 2 times 7\end{align*}\\\\ \textsf{is }y\textsf{ a multiple of }\\20\textsf{ and }28?$

Is y a multiple of both 20 and 28?

Yes

$A LaTex expression showing \begin{align*}r &= 5 times 7 to the power of 3 \\\\[-0.5em]70 &= 2 times 5 times 7\\[-0.5em]343 &= 7 to the power of 3 \end{align*}\\\\ \textsf{is }r\textsf{ a multiple of }\\70\textsf{ and }343?$

Is r a multiple of both 70 and 343?

Yes

$A LaTex expression showing \begin{align*}d &= 3 times 5 times 7 to the power of 2 \\\\[-0.5em]245 &= 5 times 7 to the power of 2 \\[-0.5em]105 &= 3 times 5 times 7\end{align*}\\\\ \textsf{is }d\textsf{ a multiple of }\\245\textsf{ and }105?$

Is d a multiple of both 245 and 105?

Yes

$A LaTex expression showing \begin{align*}p &= 5 to the power of 3 times 7\\\\[-0.5em]105 &= 3 times 5 times 7\\[-0.5em]175 &= 5 to the power of 2 times 7\end{align*}\\\\ \textsf{is }p\textsf{ a multiple of }\\105\textsf{ and }175?$

Is p a multiple of both 105 and 175?

Yes

$A LaTex expression showing \begin{align*}z &= 3 to the power of 2 times 5 to the power of 2 \\\\[-0.5em]45 &= 3 to the power of 2 times 5\\[-0.5em]75 &= 3 times 5 to the power of 2 \end{align*}\\\\ \textsf{is }z\textsf{ a multiple of }\\45\textsf{ and }75?$

Is z a multiple of both 45 and 75?

Yes

$A LaTex expression showing \begin{align*}b &= 2 times 3 to the power of 2 times 5\\\\[-0.5em]45 &= 3 to the power of 2 times 5\\[-0.5em]18 &= 2 times 3 to the power of 2 \end{align*}\\\\ \textsf{is }b\textsf{ a multiple of }\\45\textsf{ and }18?$

Is b a multiple of both 45 and 18?

Yes

$A LaTex expression showing \begin{align*}c &= 3 to the power of 2 times 5 times 7\\\\[-0.5em]30 &= 2 times 3 times 5\\[-0.5em]105 &= 3 times 5 times 7\end{align*}\\\\ \textsf{is }c\textsf{ a multiple of }\\30\textsf{ and }105?$

Is c a multiple of both 30 and 105?

Yes

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