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Prime Factorization - Is Number a Multiple - From Value as Factors (Level 3)

This math topic focuses on advanced skills related to prime factorization, determining if one number is a multiple of another, and understanding value representations as factors. Specifically, it entails evaluating given numbers expressed in factorized forms, to ascertain if one is a multiple of another utilizing their prime factorization. The problems provide factorized expressions for two numbers and ask if the first is a multiple of the second, offering a deeper insight into factoring and lowest common multiples. The format includes multiple-choice answers to validate understanding.

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

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Is Number a Multiple - From Value as Factors

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Is 270 a multiple of 189

270=2⋅33⋅5189=33⋅7is 270 a multiple of 189?\begin{align*}270 &= 2 \cdot 3^3 \cdot 5\\[-0.5em]189 &= 3^3 \cdot 7\end{align*}\\\\ \textsf{is }270\textsf{ a multiple of }189?

Prime Factorization - Is Number a Multiple - From Value as Factors Worksheet

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Math worksheet on 'Prime Factorization - Is Number a Multiple - From Value 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*}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\end{align*}\\\\ \textsf{is }700\textsf{ a multiple of }140?
Is 700 a multiple of 140
a
Yes
b
No
2
A LaTex expression showing \begin{align*}420 &= 2 to the power of 2 times 3 times 5 times 7\\[-0.5em]330 &= 2 times 3 times 5 times 11\end{align*}\\\\ \textsf{is }420\textsf{ a multiple of }330?
Is 420 a multiple of 330
a
Yes
b
No
3
A LaTex expression showing \begin{align*}252 &= 2 to the power of 2 times 3 to the power of 2 times 7\\[-0.5em]126 &= 2 times 3 to the power of 2 times 7\end{align*}\\\\ \textsf{is }252\textsf{ a multiple of }126?
Is 252 a multiple of 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]60 &= 2 to the power of 2 times 3 times 5\end{align*}\\\\ \textsf{is }420\textsf{ a multiple of }60?
Is 420 a multiple of 60
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]350 &= 2 times 5 to the power of 2 times 7\end{align*}\\\\ \textsf{is }700\textsf{ a multiple of }350?
Is 700 a multiple of 350
a
Yes
b
No
6
A LaTex expression showing \begin{align*}280 &= 2 to the power of 3 times 5 times 7\\[-0.5em]56 &= 2 to the power of 3 times 7\end{align*}\\\\ \textsf{is }280\textsf{ a multiple of }56?
Is 280 a multiple of 56
a
Yes
b
No
7
A LaTex expression showing \begin{align*}1050 &= 2 times 3 times 5 to the power of 2 times 7\\[-0.5em]525 &= 3 times 5 to the power of 2 times 7\end{align*}\\\\ \textsf{is }1050\textsf{ a multiple of }525?
Is 1050 a multiple of 525
a
Yes
b
No