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

This math topic focuses on advanced factoring and determining if one number is a factor of another using prime factorization. It delves into comparing the prime factors of two numbers to establish whether one number can completely divide the other without leaving a remainder. Each problem presents two numbers with their prime factorizations and asks if the first number is a factor of the second. The implicit skills practiced include prime factorization, understanding exponents in prime factors, and fundamental divisibility rules within the context of advanced factoring and greatest common factors.

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 1029 a factor of 2058

1029=3⋅732058=2⋅3⋅73is 1029 a factor of2058?\begin{align*}1029 &= 3 \cdot 7^3\\[-0.5em]2058 &= 2 \cdot 3 \cdot 7^3\end{align*}\\\\ \textsf{is }1029\textsf{ a factor of}\\2058?

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 3)'. Part of a broader unit on 'Factoring and Greatest Common Factor - Advanced' Learn online: app.mobius.academy/math/units/factoring_and_greatest_common_factor_advanced/
1
A LaTex expression showing \begin{align*}126 &= 2 times 3 to the power of 2 times 7\\[-0.5em]630 &= 2 times 3 to the power of 2 times 5 times 7\end{align*}\\\\ \textsf{is }126\textsf{ a factor of}\\630?
Is 126 a factor of 630
a
Yes
b
No
2
A LaTex expression showing \begin{align*}140 &= 2 to the power of 2 times 5 times 7\\[-0.5em]420 &= 2 to the power of 2 times 3 times 5 times 7\end{align*}\\\\ \textsf{is }140\textsf{ a factor of}\\420?
Is 140 a factor of 420
a
Yes
b
No
3
A LaTex expression showing \begin{align*}1715 &= 5 times 7 to the power of 3 \\[-0.5em]3430 &= 2 times 5 times 7 to the power of 3 \end{align*}\\\\ \textsf{is }1715\textsf{ a factor of}\\3430?
Is 1715 a factor of 3430
a
Yes
b
No
4
A LaTex expression showing \begin{align*}196 &= 2 to the power of 2 times 7 to the power of 2 \\[-0.5em]588 &= 2 to the power of 2 times 3 times 7 to the power of 2 \end{align*}\\\\ \textsf{is }196\textsf{ a factor of}\\588?
Is 196 a factor of 588
a
Yes
b
No
5
A LaTex expression showing \begin{align*}210 &= 2 times 3 times 5 times 7\\[-0.5em]4290 &= 2 times 3 times 5 times 11 times 13\end{align*}\\\\ \textsf{is }210\textsf{ a factor of}\\4290?
Is 210 a factor of 4290
a
Yes
b
No
6
A LaTex expression showing \begin{align*}210 &= 2 times 3 times 5 times 7\\[-0.5em]10010 &= 2 times 5 times 7 times 11 times 13\end{align*}\\\\ \textsf{is }210\textsf{ a factor of}\\10010?
Is 210 a factor of 10010
a
Yes
b
No
7
A LaTex expression showing \begin{align*}1029 &= 3 times 7 to the power of 3 \\[-0.5em]2058 &= 2 times 3 times 7 to the power of 3 \end{align*}\\\\ \textsf{is }1029\textsf{ a factor of}\\2058?
Is 1029 a factor of 2058
a
Yes
b
No