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Prime Factorization - Is Number a Multiple of Both - From Values as Factors (Level 1)

This math topic focuses on practicing prime factorization and evaluating whether a given number is a multiple of two other numbers through the use of factor trees and prime exponents. It is part of a broader unit covering factoring and calculating the lowest common multiple. Problems entail determining if one number can be divided evenly by two others based on their prime factorizations, enhancing understanding of multiples, divisibility, and prime factors in a systematic manner. Each problem requires analyzing the factorization of numbers and applying this to assess divisibility conditions.

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

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Is 70 a multiple of both 10 and 35?

70=2⋅5⋅710=2⋅535=5⋅7is 70 a multiple of 10 and 35?\begin{align*}70 &= 2 \cdot 5 \cdot 7\\[-0.5em]10 &= 2 \cdot 5\\[-0.5em]35 &= 5 \cdot 7\end{align*}\\\\ \textsf{is }70\textsf{ a multiple of }\\10\textsf{ and }35?

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 1)'. 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*}98 &= 2 times 7 to the power of 2 \\[-0.5em]26 &= 2 times 13\\[-0.5em]14 &= 2 times 7\end{align*}\\\\ \textsf{is }98\textsf{ a multiple of }\\26\textsf{ and }14?
Is 98 a multiple of both 26 and 14?
a
Yes
b
No
2
A LaTex expression showing \begin{align*}105 &= 3 times 5 times 7\\[-0.5em]21 &= 3 times 7\\[-0.5em]15 &= 3 times 5\end{align*}\\\\ \textsf{is }105\textsf{ a multiple of }\\21\textsf{ and }15?
Is 105 a multiple of both 21 and 15?
a
Yes
b
No
3
A LaTex expression showing \begin{align*}28 &= 2 to the power of 2 times 7\\[-0.5em]21 &= 3 times 7\\[-0.5em]4 &= 2 to the power of 2 \end{align*}\\\\ \textsf{is }28\textsf{ a multiple of }\\21\textsf{ and }4?
Is 28 a multiple of both 21 and 4?
a
Yes
b
No
4
A LaTex expression showing \begin{align*}20 &= 2 to the power of 2 times 5\\[-0.5em]4 &= 2 to the power of 2 \\[-0.5em]10 &= 2 times 5\end{align*}\\\\ \textsf{is }20\textsf{ a multiple of }\\4\textsf{ and }10?
Is 20 a multiple of both 4 and 10?
a
Yes
b
No
5
A LaTex expression showing \begin{align*}75 &= 3 times 5 to the power of 2 \\[-0.5em]15 &= 3 times 5\\[-0.5em]25 &= 5 to the power of 2 \end{align*}\\\\ \textsf{is }75\textsf{ a multiple of }\\15\textsf{ and }25?
Is 75 a multiple of both 15 and 25?
a
Yes
b
No
6
A LaTex expression showing \begin{align*}175 &= 5 to the power of 2 times 7\\[-0.5em]10 &= 2 times 5\\[-0.5em]35 &= 5 times 7\end{align*}\\\\ \textsf{is }175\textsf{ a multiple of }\\10\textsf{ and }35?
Is 175 a multiple of both 10 and 35?
a
Yes
b
No
7
A LaTex expression showing \begin{align*}42 &= 2 times 3 times 7\\[-0.5em]22 &= 2 times 11\\[-0.5em]21 &= 3 times 7\end{align*}\\\\ \textsf{is }42\textsf{ a multiple of }\\22\textsf{ and }21?
Is 42 a multiple of both 22 and 21?
a
Yes
b
No