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Prime Factorization - Is Number a Multiple of Both - From Values as Factors (Level 2)

This math topic involves applying prime factorization to determine if one number is a multiple of two others. Problems require the use of factoring skills to break numbers down into their prime factors, and an understanding of multiples to determine the relationship between numbers. The central theme of these problems is to assess whether a given number, after its prime factors have been exposed, is a multiple of both of two other factored numbers simultaneously, which is part of practicing Lowest Common Multiple calculation. Each question displays the prime factorization of three numbers and asks if the first is a multiple of the other two.

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

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Is Number a Multiple of Both - From Values as Factors

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

Is 875 a multiple of both 70 and 175?

875=53⋅770=2⋅5⋅7175=52⋅7is 875 a multiple of 70 and 175?\begin{align*}875 &= 5^3 \cdot 7\\[-0.5em]70 &= 2 \cdot 5 \cdot 7\\[-0.5em]175 &= 5^2 \cdot 7\end{align*}\\\\ \textsf{is }875\textsf{ a multiple of }\\70\textsf{ and }175?

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

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Math worksheet on 'Prime Factorization - Is Number a Multiple of Both - From Values as Factors (Level 2)'. Part of a broader unit on 'Factoring and Venn Factor Diagrams - Practice' Learn online: app.mobius.academy/math/units/factoring_and_venn_diagrams_practice/
1
A LaTex expression showing \begin{align*}350 &= 2 times 5 to the power of 2 times 7\\[-0.5em]70 &= 2 times 5 times 7\\[-0.5em]50 &= 2 times 5 to the power of 2 \end{align*}\\\\ \textsf{is }350\textsf{ a multiple of }\\70\textsf{ and }50?
Is 350 a multiple of both 70 and 50?
a
Yes
b
No
2
A LaTex expression showing \begin{align*}315 &= 3 to the power of 2 times 5 times 7\\[-0.5em]63 &= 3 to the power of 2 times 7\\[-0.5em]105 &= 3 times 5 times 7\end{align*}\\\\ \textsf{is }315\textsf{ a multiple of }\\63\textsf{ and }105?
Is 315 a multiple of both 63 and 105?
a
Yes
b
No
3
A LaTex expression showing \begin{align*}735 &= 3 times 5 times 7 to the power of 2 \\[-0.5em]357 &= 3 times 7 times 17\\[-0.5em]105 &= 3 times 5 times 7\end{align*}\\\\ \textsf{is }735\textsf{ a multiple of }\\357\textsf{ and }105?
Is 735 a multiple of both 357 and 105?
a
Yes
b
No
4
A LaTex expression showing \begin{align*}210 &= 2 times 3 times 5 times 7\\[-0.5em]78 &= 2 times 3 times 13\\[-0.5em]30 &= 2 times 3 times 5\end{align*}\\\\ \textsf{is }210\textsf{ a multiple of }\\78\textsf{ and }30?
Is 210 a multiple of both 78 and 30?
a
Yes
b
No
5
A LaTex expression showing \begin{align*}875 &= 5 to the power of 3 times 7\\[-0.5em]50 &= 2 times 5 to the power of 2 \\[-0.5em]175 &= 5 to the power of 2 times 7\end{align*}\\\\ \textsf{is }875\textsf{ a multiple of }\\50\textsf{ and }175?
Is 875 a multiple of both 50 and 175?
a
Yes
b
No
6
A LaTex expression showing \begin{align*}350 &= 2 times 5 to the power of 2 times 7\\[-0.5em]175 &= 5 to the power of 2 times 7\\[-0.5em]70 &= 2 times 5 times 7\end{align*}\\\\ \textsf{is }350\textsf{ a multiple of }\\175\textsf{ and }70?
Is 350 a multiple of both 175 and 70?
a
Yes
b
No
7
A LaTex expression showing \begin{align*}54 &= 2 times 3 to the power of 3 \\[-0.5em]42 &= 2 times 3 times 7\\[-0.5em]27 &= 3 to the power of 3 \end{align*}\\\\ \textsf{is }54\textsf{ a multiple of }\\42\textsf{ and }27?
Is 54 a multiple of both 42 and 27?
a
Yes
b
No