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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

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

Is 225 a factor of 1050

225=32⋅521050=2⋅3⋅52⋅7is 225 a factor of1050?\begin{align*}225 &= 3^2 \cdot 5^2\\\\[-0.5em]1050 &= 2 \cdot 3 \cdot 5^2 \cdot 7\end{align*}\\\\ \textsf{is }225\textsf{ a factor of}\\1050?

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 - Intro' Learn online: app.mobius.academy/math/units/factoring_and_greatest_common_factor_intro/
1
A LaTex expression showing \begin{align*}210 &= 2 times 3 times 5 times 7\\\\[-0.5em]6006 &= 2 times 3 times 7 times 11 times 13\end{align*}\\\\ \textsf{is }210\textsf{ a factor of}\\6006?
Is 210 a factor of 6006
a
Yes
b
No
2
A LaTex expression showing \begin{align*}189 &= 3 to the power of 3 times 7\\\\[-0.5em]378 &= 2 times 3 to the power of 3 times 7\end{align*}\\\\ \textsf{is }189\textsf{ a factor of}\\378?
Is 189 a factor of 378
a
Yes
b
No
3
A LaTex expression showing \begin{align*}150 &= 2 times 3 times 5 to the power of 2 \\\\[-0.5em]1050 &= 2 times 3 times 5 to the power of 2 times 7\end{align*}\\\\ \textsf{is }150\textsf{ a factor of}\\1050?
Is 150 a factor of 1050
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]420 &= 2 to the power of 2 times 3 times 5 times 7\end{align*}\\\\ \textsf{is }196\textsf{ a factor of}\\420?
Is 196 a factor of 420
a
Yes
b
No
5
A LaTex expression showing \begin{align*}90 &= 2 times 3 to the power of 2 times 5\\\\[-0.5em]630 &= 2 times 3 to the power of 2 times 5 times 7\end{align*}\\\\ \textsf{is }90\textsf{ a factor of}\\630?
Is 90 a factor of 630
a
Yes
b
No
6
A LaTex expression showing \begin{align*}294 &= 2 times 3 times 7 to the power of 2 \\\\[-0.5em]5390 &= 2 times 5 times 7 to the power of 2 times 11\end{align*}\\\\ \textsf{is }294\textsf{ a factor of}\\5390?
Is 294 a factor of 5390
a
Yes
b
No
7
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