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

This math topic focuses on determining whether one number is a factor of another through prime factorization. It includes problems where students must compare the prime factorization of two numbers to see if the factors of the first number completely appear in the second. The problems typically format as "Is [first number] a factor of [second number]?" with a structured breakdown of each number’s prime factors. The topic is a part of broader units on factoring and finding the greatest common factor, enhancing students' understanding of number relationships and divisibility rules.

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

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Is Number a Factor - From Value as Factors

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Is 98 a factor of 210

98=2⋅72210=2⋅3⋅5⋅7is 98 a factor of210?\begin{align*}98 &= 2 \cdot 7^2\\[-0.5em]210 &= 2 \cdot 3 \cdot 5 \cdot 7\end{align*}\\\\ \textsf{is }98\textsf{ a factor of}\\210?

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

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Math worksheet on 'Prime Factorization - Is Number a Factor - From Value as Factors (Level 2)'. Part of a broader unit on 'Digits and Divisibility - Intro' Learn online: app.mobius.academy/math/units/digits_and_divisibility_intro/
1
A LaTex expression showing \begin{align*}18 &= 2 times 3 to the power of 2 \\[-0.5em]210 &= 2 times 3 times 5 times 7\end{align*}\\\\ \textsf{is }18\textsf{ a factor of}\\210?
Is 18 a factor of 210
a
Yes
b
No
2
A LaTex expression showing \begin{align*}175 &= 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 }175\textsf{ a factor of}\\350?
Is 175 a factor of 350
a
Yes
b
No
3
A LaTex expression showing \begin{align*}70 &= 2 times 5 times 7\\[-0.5em]210 &= 2 times 3 times 5 times 7\end{align*}\\\\ \textsf{is }70\textsf{ a factor of}\\210?
Is 70 a factor of 210
a
Yes
b
No
4
A LaTex expression showing \begin{align*}30 &= 2 times 3 times 5\\[-0.5em]1155 &= 3 times 5 times 7 times 11\end{align*}\\\\ \textsf{is }30\textsf{ a factor of}\\1155?
Is 30 a factor of 1155
a
Yes
b
No
5
A LaTex expression showing \begin{align*}12 &= 2 to the power of 2 times 3\\[-0.5em]60 &= 2 to the power of 2 times 3 times 5\end{align*}\\\\ \textsf{is }12\textsf{ a factor of}\\60?
Is 12 a factor of 60
a
Yes
b
No
6
A LaTex expression showing \begin{align*}105 &= 3 times 5 times 7\\[-0.5em]770 &= 2 times 5 times 7 times 11\end{align*}\\\\ \textsf{is }105\textsf{ a factor of}\\770?
Is 105 a factor of 770
a
Yes
b
No
7
A LaTex expression showing \begin{align*}20 &= 2 to the power of 2 times 5\\[-0.5em]84 &= 2 to the power of 2 times 3 times 7\end{align*}\\\\ \textsf{is }20\textsf{ a factor of}\\84?
Is 20 a factor of 84
a
Yes
b
No