Prime Factorization - Is Integer a Factor of Both - From Values as Factors (Level 3)

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

$A LaTex expression showing \begin{align*}250 &= p times r to the power of 3 \\\\[-0.5em]750 &= 2 times 3 times 5 to the power of 3 \\[-0.5em]1750 &= 2 times 5 to the power of 3 times 7\end{align*}\\\\ \textsf{is }250\textsf{ a factor of}\\750\textsf{ and }1750?$

Is 250 a factor of both 750 and 1750?

Yes

$A LaTex expression showing \begin{align*}210 &= d times r times z times p\\\\[-0.5em]6006 &= 2 times 3 times 7 times 11 times 13\\[-0.5em]13090 &= 2 times 5 times 7 times 11 times 17\end{align*}\\\\ \textsf{is }210\textsf{ a factor of}\\6006\textsf{ and }13090?$

Is 210 a factor of both 6006 and 13090?

Yes

$A LaTex expression showing \begin{align*}100 &= b to the power of 2 times c to the power of 2 \\\\[-0.5em]300 &= 2 to the power of 2 times 3 times 5 to the power of 2 \\[-0.5em]700 &= 2 to the power of 2 times 5 to the power of 2 times 7\end{align*}\\\\ \textsf{is }100\textsf{ a factor of}\\300\textsf{ and }700?$

Is 100 a factor of both 300 and 700?

Yes

$A LaTex expression showing \begin{align*}1225 &= r to the power of 2 times b to the power of 2 \\\\[-0.5em]2450 &= 2 times 5 to the power of 2 times 7 to the power of 2 \\[-0.5em]3675 &= 3 times 5 to the power of 2 times 7 to the power of 2 \end{align*}\\\\ \textsf{is }1225\textsf{ a factor of}\\2450\textsf{ and }3675?$

Is 1225 a factor of both 2450 and 3675?

Yes

$A LaTex expression showing \begin{align*}525 &= r times x to the power of 2 times p\\\\[-0.5em]1050 &= 2 times 3 times 5 to the power of 2 times 7\\[-0.5em]5775 &= 3 times 5 to the power of 2 times 7 times 11\end{align*}\\\\ \textsf{is }525\textsf{ a factor of}\\1050\textsf{ and }5775?$

Is 525 a factor of both 1050 and 5775?

Yes

$A LaTex expression showing \begin{align*}60 &= m to the power of 2 times p times d\\\\[-0.5em]420 &= 2 to the power of 2 times 3 times 5 times 7\\[-0.5em]660 &= 2 to the power of 2 times 3 times 5 times 11\end{align*}\\\\ \textsf{is }60\textsf{ a factor of}\\420\textsf{ and }660?$

Is 60 a factor of both 420 and 660?

Yes

$A LaTex expression showing \begin{align*}56 &= p to the power of 3 times z\\\\[-0.5em]420 &= 2 to the power of 2 times 3 times 5 times 7\\[-0.5em]924 &= 2 to the power of 2 times 3 times 7 times 11\end{align*}\\\\ \textsf{is }56\textsf{ a factor of}\\420\textsf{ and }924?$

Is 56 a factor of both 420 and 924?

Yes

$A LaTex expression showing \begin{align*}315 &= c to the power of 2 times p times x\\\\[-0.5em]2310 &= 2 times 3 times 5 times 7 times 11\\[-0.5em]1638 &= 2 times 3 to the power of 2 times 7 times 13\end{align*}\\\\ \textsf{is }315\textsf{ a factor of}\\2310\textsf{ and }1638?$

Is 315 a factor of both 2310 and 1638?

Yes

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