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Prime Factorization

Is Number a Multiple - From Variable as Factors (Level 3)

This math topic practices advanced skills related to prime factorization, checking if one number is a multiple of another, and operations using variables expressed as factors. The problems involve analyzing expressions with variables defined as products of primes raised to powers, and determining if one expression (in terms of its numeric evaluation) is a multiple of another. It covers key concepts in factoring and understanding lowest common multiples at an advanced level.

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

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Prime Factorization - Is Number a Multiple - From Variable as Factors Worksheet

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Prime Factorization - Is Number a Multiple - From Variable as Factors
1
A LaTex expression showing \begin{align*}c &= 2 to the power of 2 times 3 times 5 times 7\\\\[-0.5em]60 &= 2 to the power of 2 times 3 times 5\end{align*}\\\\ \textsf{is }c\textsf{ a multiple of }60?
Is c a multiple of 60
a
Yes
b
No
2
A LaTex expression showing \begin{align*}z &= 2 to the power of 2 times 3 times 5 to the power of 2 \\\\[-0.5em]150 &= 2 times 3 times 5 to the power of 2 \end{align*}\\\\ \textsf{is }z\textsf{ a multiple of }150?
Is z a multiple of 150
a
Yes
b
No
3
A LaTex expression showing \begin{align*}b &= 2 to the power of 2 times 3 times 7 to the power of 2 \\\\[-0.5em]196 &= 2 to the power of 2 times 7 to the power of 2 \end{align*}\\\\ \textsf{is }b\textsf{ a multiple of }196?
Is b a multiple of 196
a
Yes
b
No
4
A LaTex expression showing \begin{align*}d &= 2 to the power of 2 times 3 to the power of 2 times 7\\\\[-0.5em]84 &= 2 to the power of 2 times 3 times 7\end{align*}\\\\ \textsf{is }d\textsf{ a multiple of }84?
Is d a multiple of 84
a
Yes
b
No
5
A LaTex expression showing \begin{align*}z &= 5 to the power of 2 times 7 to the power of 3 \\\\[-0.5em]2695 &= 5 times 7 to the power of 2 times 11\end{align*}\\\\ \textsf{is }z\textsf{ a multiple of }2695?
Is z a multiple of 2695
a
Yes
b
No
6
A LaTex expression showing \begin{align*}z &= 2 to the power of 3 times 5 times 7\\\\[-0.5em]60 &= 2 to the power of 2 times 3 times 5\end{align*}\\\\ \textsf{is }z\textsf{ a multiple of }60?
Is z a multiple of 60
a
Yes
b
No
7
A LaTex expression showing \begin{align*}z &= 2 to the power of 2 times 3 times 5 times 7\\\\[-0.5em]210 &= 2 times 3 times 5 times 7\end{align*}\\\\ \textsf{is }z\textsf{ a multiple of }210?
Is z a multiple of 210
a
Yes
b
No
8
A LaTex expression showing \begin{align*}r &= 2 times 3 times 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 }r\textsf{ a multiple of }350?
Is r a multiple of 350
a
Yes
b
No