HomePricing
Sign InJoin

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.

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 x a multiple of both 77 and 49?

x=3⋅7277=7⋅1149=72is x a multiple of 77 and 49?\begin{align*}x &= 3 \cdot 7^2\\[-0.5em]77 &= 7 \cdot 11\\[-0.5em]49 &= 7^2\end{align*}\\\\ \textsf{is }x\textsf{ a multiple of }\\77\textsf{ and }49?

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

Mobius Math Club logo
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 - Intro' Learn online: app.mobius.academy/math/units/factoring_and_lowest_common_multiple_intro/
1
A LaTex expression showing \begin{align*}z &= 3 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 }z\textsf{ a multiple of }\\15\textsf{ and }49?
Is z a multiple of both 15 and 49?
a
Yes
b
No
2
A LaTex expression showing \begin{align*}b &= 3 times 5 times 7\\[-0.5em]21 &= 3 times 7\\[-0.5em]35 &= 5 times 7\end{align*}\\\\ \textsf{is }b\textsf{ a multiple of }\\21\textsf{ and }35?
Is b a multiple of both 21 and 35?
a
Yes
b
No
3
A LaTex expression showing \begin{align*}x &= 5 to the power of 2 times 7\\[-0.5em]35 &= 5 times 7\\[-0.5em]25 &= 5 to the power of 2 \end{align*}\\\\ \textsf{is }x\textsf{ a multiple of }\\35\textsf{ and }25?
Is x a multiple of both 35 and 25?
a
Yes
b
No
4
A LaTex expression showing \begin{align*}c &= 2 to the power of 2 times 3\\[-0.5em]6 &= 2 times 3\\[-0.5em]4 &= 2 to the power of 2 \end{align*}\\\\ \textsf{is }c\textsf{ a multiple of }\\6\textsf{ and }4?
Is c a multiple of both 6 and 4?
a
Yes
b
No
5
A LaTex expression showing \begin{align*}d &= 2 times 5 times 7\\[-0.5em]55 &= 5 times 11\\[-0.5em]10 &= 2 times 5\end{align*}\\\\ \textsf{is }d\textsf{ a multiple of }\\55\textsf{ and }10?
Is d a multiple of both 55 and 10?
a
Yes
b
No
6
A LaTex expression showing \begin{align*}r &= 3 times 5 times 7\\[-0.5em]39 &= 3 times 13\\[-0.5em]35 &= 5 times 7\end{align*}\\\\ \textsf{is }r\textsf{ a multiple of }\\39\textsf{ and }35?
Is r a multiple of both 39 and 35?
a
Yes
b
No
7
A LaTex expression showing \begin{align*}c &= 2 to the power of 2 times 7\\[-0.5em]6 &= 2 times 3\\[-0.5em]14 &= 2 times 7\end{align*}\\\\ \textsf{is }c\textsf{ a multiple of }\\6\textsf{ and }14?
Is c a multiple of both 6 and 14?
a
Yes
b
No