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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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*}135 &= 3 to the power of 3 times 5\\\\[-0.5em]270 &= 2 times 3 to the power of 3 times 5\end{align*}\\\\ \textsf{is }135\textsf{ a factor of}\\270?
Is 135 a factor of 270
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*}315 &= 3 to the power of 2 times 5 times 7\\\\[-0.5em]2310 &= 2 times 3 times 5 times 7 times 11\end{align*}\\\\ \textsf{is }315\textsf{ a factor of}\\2310?
Is 315 a factor of 2310
a
Yes
b
No
4
A LaTex expression showing \begin{align*}210 &= 2 times 3 times 5 times 7\\\\[-0.5em]15015 &= 3 times 5 times 7 times 11 times 13\end{align*}\\\\ \textsf{is }210\textsf{ a factor of}\\15015?
Is 210 a factor of 15015
a
Yes
b
No
5
A LaTex expression showing \begin{align*}140 &= 2 to the power of 2 times 5 times 7\\\\[-0.5em]660 &= 2 to the power of 2 times 3 times 5 times 11\end{align*}\\\\ \textsf{is }140\textsf{ a factor of}\\660?
Is 140 a factor of 660
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*}350 &= 2 times 5 to the power of 2 times 7\\\\[-0.5em]5775 &= 3 times 5 to the power of 2 times 7 times 11\end{align*}\\\\ \textsf{is }350\textsf{ a factor of}\\5775?
Is 350 a factor of 5775
a
Yes
b
No
8
A LaTex expression showing \begin{align*}84 &= 2 to the power of 2 times 3 times 7\\\\[-0.5em]420 &= 2 to the power of 2 times 3 times 5 times 7\end{align*}\\\\ \textsf{is }84\textsf{ a factor of}\\420?
Is 84 a factor of 420
a
Yes
b
No