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Prime Factorization

Is Number a Multiple of Both - From Variables as Factors (Level 1)

This math topic covers skills in prime factorization, identifying multiples, and using variables as factors. The problems involve determining whether a given product expressed through a combination of primes and variables is a multiple of other specified products. Each question presents expressions and asks if one is a multiple of the others, with options for yes or no answers. The focus is on understanding factorization and the principles of multiples within the context of higher-level arithmetic operations, notably within a unit focused on factoring and finding the lowest common multiples.

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 of Both - From Variables as Factors Worksheet

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Prime Factorization - Is Number a Multiple of Both - From Variables as Factors
1
A LaTex expression showing \begin{align*}n &= 3 times 7 to the power of 2 \\\\[-0.5em]35 &= 5 times 7\\[-0.5em]21 &= 3 times 7\end{align*}\\\\ \textsf{is }n\textsf{ a multiple of }\\35\textsf{ and }21?
Is n a multiple of both 35 and 21?
a
Yes
b
No
2
A LaTex expression showing \begin{align*}r &= 3 to the power of 2 times 5\\\\[-0.5em]9 &= 3 to the power of 2 \\[-0.5em]15 &= 3 times 5\end{align*}\\\\ \textsf{is }r\textsf{ a multiple of }\\9\textsf{ and }15?
Is r a multiple of both 9 and 15?
a
Yes
b
No
3
A LaTex expression showing \begin{align*}d &= 2 times 5 times 7\\\\[-0.5em]14 &= 2 times 7\\[-0.5em]10 &= 2 times 5\end{align*}\\\\ \textsf{is }d\textsf{ a multiple of }\\14\textsf{ and }10?
Is d a multiple of both 14 and 10?
a
Yes
b
No
4
A LaTex expression showing \begin{align*}n &= 2 times 5 times 7\\\\[-0.5em]10 &= 2 times 5\\[-0.5em]35 &= 5 times 7\end{align*}\\\\ \textsf{is }n\textsf{ a multiple of }\\10\textsf{ and }35?
Is n a multiple of both 10 and 35?
a
Yes
b
No
5
A LaTex expression showing \begin{align*}p &= 2 to the power of 2 times 7\\\\[-0.5em]4 &= 2 to the power of 2 \\[-0.5em]14 &= 2 times 7\end{align*}\\\\ \textsf{is }p\textsf{ a multiple of }\\4\textsf{ and }14?
Is p a multiple of both 4 and 14?
a
Yes
b
No
6
A LaTex expression showing \begin{align*}b &= 3 times 5 to the power of 2 \\\\[-0.5em]33 &= 3 times 11\\[-0.5em]25 &= 5 to the power of 2 \end{align*}\\\\ \textsf{is }b\textsf{ a multiple of }\\33\textsf{ and }25?
Is b a multiple of both 33 and 25?
a
Yes
b
No
7
A LaTex expression showing \begin{align*}c &= 5 times 7 to the power of 2 \\\\[-0.5em]21 &= 3 times 7\\[-0.5em]35 &= 5 times 7\end{align*}\\\\ \textsf{is }c\textsf{ a multiple of }\\21\textsf{ and }35?
Is c a multiple of both 21 and 35?
a
Yes
b
No
8
A LaTex expression showing \begin{align*}p &= 3 to the power of 2 times 5\\\\[-0.5em]21 &= 3 times 7\\[-0.5em]15 &= 3 times 5\end{align*}\\\\ \textsf{is }p\textsf{ a multiple of }\\21\textsf{ and }15?
Is p a multiple of both 21 and 15?
a
Yes
b
No