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Prime Factorization - Is Number a Multiple - From Value as Factors (Level 2)

This math topic includes exercises on prime factorization and checking if one number is a multiple of another based on their prime factors. The problems involve breaking down each given number into its prime components and verifying if all factors of the divisor are present in the dividend with at least the same multiplicity. It falls under a larger unit on factoring and finding the lowest common multiple, designed to enhance students' understanding of these concepts through practical application. Each question offers a clear setup through given statements with options for a binary 'Yes' or 'No' answer, indicating whether one number is a multiple of the other.

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 140 a multiple of 28

140=22⋅5⋅728=22⋅7is 140 a multiple of 28?\begin{align*}140 &= 2^2 \cdot 5 \cdot 7\\[-0.5em]28 &= 2^2 \cdot 7\end{align*}\\\\ \textsf{is }140\textsf{ a multiple of }28?

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 2)'. Part of a broader unit on 'Factoring and Venn Factor Diagrams - Practice' Learn online: app.mobius.academy/math/units/factoring_and_venn_diagrams_practice/
1
A LaTex expression showing \begin{align*}294 &= 2 times 3 times 7 to the power of 2 \\[-0.5em]98 &= 2 times 7 to the power of 2 \end{align*}\\\\ \textsf{is }294\textsf{ a multiple of }98?
Is 294 a multiple of 98
a
Yes
b
No
2
A LaTex expression showing \begin{align*}350 &= 2 times 5 to the power of 2 times 7\\[-0.5em]70 &= 2 times 5 times 7\end{align*}\\\\ \textsf{is }350\textsf{ a multiple of }70?
Is 350 a multiple of 70
a
Yes
b
No
3
A LaTex expression showing \begin{align*}140 &= 2 to the power of 2 times 5 times 7\\[-0.5em]70 &= 2 times 5 times 7\end{align*}\\\\ \textsf{is }140\textsf{ a multiple of }70?
Is 140 a multiple of 70
a
Yes
b
No
4
A LaTex expression showing \begin{align*}525 &= 3 times 5 to the power of 2 times 7\\[-0.5em]275 &= 5 to the power of 2 times 11\end{align*}\\\\ \textsf{is }525\textsf{ a multiple of }275?
Is 525 a multiple of 275
a
Yes
b
No
5
A LaTex expression showing \begin{align*}135 &= 3 to the power of 3 times 5\\[-0.5em]27 &= 3 to the power of 3 \end{align*}\\\\ \textsf{is }135\textsf{ a multiple of }27?
Is 135 a multiple of 27
a
Yes
b
No
6
A LaTex expression showing \begin{align*}84 &= 2 to the power of 2 times 3 times 7\\[-0.5em]12 &= 2 to the power of 2 times 3\end{align*}\\\\ \textsf{is }84\textsf{ a multiple of }12?
Is 84 a multiple of 12
a
Yes
b
No
7
A LaTex expression showing \begin{align*}196 &= 2 to the power of 2 times 7 to the power of 2 \\[-0.5em]98 &= 2 times 7 to the power of 2 \end{align*}\\\\ \textsf{is }196\textsf{ a multiple of }98?
Is 196 a multiple of 98
a
Yes
b
No