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

This math topic focuses on advanced concepts of prime factorization and checking whether one number is a multiple of others, using their prime factorized forms. It involves determining if a primary number is a multiple of two other numbers by analyzing their factorized structures, as presented in the format of prime factors raised to appropriate exponents. Additionally, this topic falls under a broader unit on factoring and finding the lowest common multiple, targeting an advanced understanding of these concepts. Each problem presents a situation to decide if one number is a multiple of the others provided, with a choice of 'Yes' or 'No' as answers.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Is Number a Multiple of Both - From Values as Factors

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Is 700 a multiple of both 150 and 100?

700=22⋅52⋅7150=2⋅3⋅52100=22⋅52is 700 a multiple of 150 and 100?\begin{align*}700 &= 2^2 \cdot 5^2 \cdot 7\\[-0.5em]150 &= 2 \cdot 3 \cdot 5^2\\[-0.5em]100 &= 2^2 \cdot 5^2\end{align*}\\\\ \textsf{is }700\textsf{ a multiple of }\\150\textsf{ and }100?

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

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Math worksheet on 'Prime Factorization - Is Number a Multiple of Both - From Values as Factors (Level 3)'. Part of a broader unit on 'Factoring and Lowest Common Multiple - Advanced' Learn online: app.mobius.academy/math/units/factoring_and_lowest_common_multiple_advanced/
1
A LaTex expression showing \begin{align*}675 &= 3 to the power of 3 times 5 to the power of 2 \\[-0.5em]525 &= 3 times 5 to the power of 2 times 7\\[-0.5em]135 &= 3 to the power of 3 times 5\end{align*}\\\\ \textsf{is }675\textsf{ a multiple of }\\525\textsf{ and }135?
Is 675 a multiple of both 525 and 135?
a
Yes
b
No
2
A LaTex expression showing \begin{align*}700 &= 2 to the power of 2 times 5 to the power of 2 times 7\\[-0.5em]150 &= 2 times 3 times 5 to the power of 2 \\[-0.5em]100 &= 2 to the power of 2 times 5 to the power of 2 \end{align*}\\\\ \textsf{is }700\textsf{ a multiple of }\\150\textsf{ and }100?
Is 700 a multiple of both 150 and 100?
a
Yes
b
No
3
A LaTex expression showing \begin{align*}630 &= 2 times 3 to the power of 2 times 5 times 7\\[-0.5em]570 &= 2 times 3 times 5 times 19\\[-0.5em]126 &= 2 times 3 to the power of 2 times 7\end{align*}\\\\ \textsf{is }630\textsf{ a multiple of }\\570\textsf{ and }126?
Is 630 a multiple of both 570 and 126?
a
Yes
b
No
4
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?
a
Yes
b
No
5
A LaTex expression showing \begin{align*}700 &= 2 to the power of 2 times 5 to the power of 2 times 7\\[-0.5em]100 &= 2 to the power of 2 times 5 to the power of 2 \\[-0.5em]140 &= 2 to the power of 2 times 5 times 7\end{align*}\\\\ \textsf{is }700\textsf{ a multiple of }\\100\textsf{ and }140?
Is 700 a multiple of both 100 and 140?
a
Yes
b
No
6
A LaTex expression showing \begin{align*}1470 &= 2 times 3 times 5 times 7 to the power of 2 \\[-0.5em]735 &= 3 times 5 times 7 to the power of 2 \\[-0.5em]210 &= 2 times 3 times 5 times 7\end{align*}\\\\ \textsf{is }1470\textsf{ a multiple of }\\735\textsf{ and }210?
Is 1470 a multiple of both 735 and 210?
a
Yes
b
No
7
A LaTex expression showing \begin{align*}4802 &= 2 times 7 to the power of 4 \\[-0.5em]2401 &= 7 to the power of 4 \\[-0.5em]686 &= 2 times 7 to the power of 3 \end{align*}\\\\ \textsf{is }4802\textsf{ a multiple of }\\2401\textsf{ and }686?
Is 4802 a multiple of both 2401 and 686?
a
Yes
b
No