Prime Factorizatio

Is Number a Multiple of Both - From Values as Factors (Level 3)

This math topic focuses on advanced concepts of prime factorization and checking whether one number is a multiple of others, using their prime factorized forms. It involves determining if a primary number is a multiple of two other numbers by analyzing their factorized structures, as presented in the format of prime factors raised to appropriate exponents. Additionally, this topic falls under a broader unit on factoring and finding the lowest common multiple, targeting an advanced understanding of these concepts. Each problem presents a situation to decide if one number is a multiple of the others provided, with a choice of 'Yes' or 'No' as answers.

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 2058 a multiple of both 1029 and 294?

\begin{align*}2058 &= 2 \cdot 3 \cdot 7^3\\\\[-0.5em]1029 &= 3 \cdot 7^3\\[-0.5em]294 &= 2 \cdot 3 \cdot 7^2\end{align*}\\\\ \textsf{is }2058\textsf{ a multiple of }\\1029\textsf{ and }294?

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

Math worksheet on 'Prime Factorization - Is Number a Multiple of Both - From Values as Factors (Level 3)'. Part of a broader unit on 'Factoring and Lowest Common Multiple - Advanced' Learn online: app.mobius.academy/math/units/factoring_and_lowest_common_multiple_advanced/

$A LaTex expression showing \begin{align*}1470 &= 2 times 3 times 5 times 7 to the power of 2 \\\\[-0.5em]210 &= 2 times 3 times 5 times 7\\[-0.5em]294 &= 2 times 3 times 7 to the power of 2 \end{align*}\\\\ \textsf{is }1470\textsf{ a multiple of }\\210\textsf{ and }294?$

Is 1470 a multiple of both 210 and 294?

Yes

$A LaTex expression showing \begin{align*}2625 &= 3 times 5 to the power of 3 times 7\\\\[-0.5em]375 &= 3 times 5 to the power of 3 \\[-0.5em]525 &= 3 times 5 to the power of 2 times 7\end{align*}\\\\ \textsf{is }2625\textsf{ a multiple of }\\375\textsf{ and }525?$

Is 2625 a multiple of both 375 and 525?

Yes

$A LaTex expression showing \begin{align*}567 &= 3 to the power of 4 times 7\\\\[-0.5em]81 &= 3 to the power of 4 \\[-0.5em]189 &= 3 to the power of 3 times 7\end{align*}\\\\ \textsf{is }567\textsf{ a multiple of }\\81\textsf{ and }189?$

Is 567 a multiple of both 81 and 189?

Yes

$A LaTex expression showing \begin{align*}120 &= 2 to the power of 3 times 3 times 5\\\\[-0.5em]60 &= 2 to the power of 2 times 3 times 5\\[-0.5em]40 &= 2 to the power of 3 times 5\end{align*}\\\\ \textsf{is }120\textsf{ a multiple of }\\60\textsf{ and }40?$

Is 120 a multiple of both 60 and 40?

Yes

$A LaTex expression showing \begin{align*}700 &= 2 to the power of 2 times 5 to the power of 2 times 7\\\\[-0.5em]140 &= 2 to the power of 2 times 5 times 7\\[-0.5em]350 &= 2 times 5 to the power of 2 times 7\end{align*}\\\\ \textsf{is }700\textsf{ a multiple of }\\140\textsf{ and }350?$

Is 700 a multiple of both 140 and 350?

Yes

$A LaTex expression showing \begin{align*}4802 &= 2 times 7 to the power of 4 \\\\[-0.5em]1274 &= 2 times 7 to the power of 2 times 13\\[-0.5em]2401 &= 7 to the power of 4 \end{align*}\\\\ \textsf{is }4802\textsf{ a multiple of }\\1274\textsf{ and }2401?$

Is 4802 a multiple of both 1274 and 2401?

Yes

$A LaTex expression showing \begin{align*}3430 &= 2 times 5 times 7 to the power of 3 \\\\[-0.5em]686 &= 2 times 7 to the power of 3 \\[-0.5em]490 &= 2 times 5 times 7 to the power of 2 \end{align*}\\\\ \textsf{is }3430\textsf{ a multiple of }\\686\textsf{ and }490?$

Is 3430 a multiple of both 686 and 490?

Yes

Prime Factorizatio

Practice:

Is Number a Multiple of Both - From Values as Factors

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