Prime Factorizatio

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.

View Unit

Is Number a Multiple of Both - From Variables as Factors

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

Is c a multiple of both 10 and 15?

\begin{align*}c &= 2 \cdot 3 \cdot 5\\\\[-0.5em]10 &= 2 \cdot 5\\[-0.5em]15 &= 3 \cdot 5\end{align*}\\\\ \textsf{is }c\textsf{ a multiple of }\\10\textsf{ and }15?

Earned ?

Prime Factorization - Is Number a Multiple of Both - From Variables as Factors Worksheet

Math worksheet on 'Prime Factorization - Is Number a Multiple of Both - From Variables as Factors (Level 1)'. Part of a broader unit on 'Factoring and Lowest Common Multiple - Practice' Learn online: app.mobius.academy/math/units/factoring_and_lowest_common_multiple_practice/

$A LaTex expression showing \begin{align*}n &= 2 times 3 times 5\\\\[-0.5em]15 &= 3 times 5\\[-0.5em]10 &= 2 times 5\end{align*}\\\\ \textsf{is }n\textsf{ a multiple of }\\15\textsf{ and }10?$

Is n a multiple of both 15 and 10?

Yes

$A LaTex expression showing \begin{align*}c &= 5 times 7 to the power of 2 \\\\[-0.5em]15 &= 3 times 5\\[-0.5em]49 &= 7 to the power of 2 \end{align*}\\\\ \textsf{is }c\textsf{ a multiple of }\\15\textsf{ and }49?$

Is c a multiple of both 15 and 49?

Yes

$A LaTex expression showing \begin{align*}m &= 3 times 5 times 7\\\\[-0.5em]35 &= 5 times 7\\[-0.5em]21 &= 3 times 7\end{align*}\\\\ \textsf{is }m\textsf{ a multiple of }\\35\textsf{ and }21?$

Is m a multiple of both 35 and 21?

Yes

$A LaTex expression showing \begin{align*}b &= 3 times 5 to the power of 2 \\\\[-0.5em]33 &= 3 times 11\\[-0.5em]25 &= 5 to the power of 2 \end{align*}\\\\ \textsf{is }b\textsf{ a multiple of }\\33\textsf{ and }25?$

Is b a multiple of both 33 and 25?

Yes

$A LaTex expression showing \begin{align*}d &= 5 times 7 to the power of 2 \\\\[-0.5em]35 &= 5 times 7\\[-0.5em]49 &= 7 to the power of 2 \end{align*}\\\\ \textsf{is }d\textsf{ a multiple of }\\35\textsf{ and }49?$

Is d a multiple of both 35 and 49?

Yes

$A LaTex expression showing \begin{align*}b &= 5 to the power of 2 times 7\\\\[-0.5em]25 &= 5 to the power of 2 \\[-0.5em]35 &= 5 times 7\end{align*}\\\\ \textsf{is }b\textsf{ a multiple of }\\25\textsf{ and }35?$

Is b a multiple of both 25 and 35?

Yes

$A LaTex expression showing \begin{align*}r &= 3 to the power of 2 times 5\\\\[-0.5em]9 &= 3 to the power of 2 \\[-0.5em]15 &= 3 times 5\end{align*}\\\\ \textsf{is }r\textsf{ a multiple of }\\9\textsf{ and }15?$

Is r a multiple of both 9 and 15?

Yes

Prime Factorizatio

Practice:

Is Number a Multiple of Both - From Variables as Factors

Prime Factorization - Is Number a Multiple of Both - From Variables as Factors Worksheet