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

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Prime Factorization - Is Number a Factor - From Value as Factors
1
A LaTex expression showing \begin{align*}70 &= 2 times 5 times 7\\\\[-0.5em]462 &= 2 times 3 times 7 times 11\end{align*}\\\\ \textsf{is }70\textsf{ a factor of}\\462?
Is 70 a factor of 462
a
Yes
b
No
2
A LaTex expression showing \begin{align*}28 &= 2 to the power of 2 times 7\\\\[-0.5em]210 &= 2 times 3 times 5 times 7\end{align*}\\\\ \textsf{is }28\textsf{ a factor of}\\210?
Is 28 a factor of 210
a
Yes
b
No
3
A LaTex expression showing \begin{align*}45 &= 3 to the power of 2 times 5\\\\[-0.5em]90 &= 2 times 3 to the power of 2 times 5\end{align*}\\\\ \textsf{is }45\textsf{ a factor of}\\90?
Is 45 a factor of 90
a
Yes
b
No
4
A LaTex expression showing \begin{align*}98 &= 2 times 7 to the power of 2 \\\\[-0.5em]735 &= 3 times 5 times 7 to the power of 2 \end{align*}\\\\ \textsf{is }98\textsf{ a factor of}\\735?
Is 98 a factor of 735
a
Yes
b
No
5
A LaTex expression showing \begin{align*}30 &= 2 times 3 times 5\\\\[-0.5em]462 &= 2 times 3 times 7 times 11\end{align*}\\\\ \textsf{is }30\textsf{ a factor of}\\462?
Is 30 a factor of 462
a
Yes
b
No
6
A LaTex expression showing \begin{align*}70 &= 2 times 5 times 7\\\\[-0.5em]330 &= 2 times 3 times 5 times 11\end{align*}\\\\ \textsf{is }70\textsf{ a factor of}\\330?
Is 70 a factor of 330
a
Yes
b
No
7
A LaTex expression showing \begin{align*}42 &= 2 times 3 times 7\\\\[-0.5em]210 &= 2 times 3 times 5 times 7\end{align*}\\\\ \textsf{is }42\textsf{ a factor of}\\210?
Is 42 a factor of 210
a
Yes
b
No
8
A LaTex expression showing \begin{align*}28 &= 2 to the power of 2 times 7\\\\[-0.5em]84 &= 2 to the power of 2 times 3 times 7\end{align*}\\\\ \textsf{is }28\textsf{ a factor of}\\84?
Is 28 a factor of 84
a
Yes
b
No