Prime Factorization - Is Number a Multiple of Both - From Values as Factors (Level 1)

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

This math topic focuses on practicing prime factorization and evaluating whether a given number is a multiple of two other numbers through the use of factor trees and prime exponents. It is part of a broader unit covering factoring and calculating the lowest common multiple. Problems entail determining if one number can be divided evenly by two others based on their prime factorizations, enhancing understanding of multiples, divisibility, and prime factors in a systematic manner. Each problem requires analyzing the factorization of numbers and applying this to assess divisibility conditions.

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 Values as Factors Worksheet

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

$A LaTex expression showing \begin{align*}75 &= 3 times 5 to the power of 2 \\\\[-0.5em]15 &= 3 times 5\\[-0.5em]25 &= 5 to the power of 2 \end{align*}\\\\ \textsf{is }75\textsf{ a multiple of }\\15\textsf{ and }25?$

Is 75 a multiple of both 15 and 25?

Yes

$A LaTex expression showing \begin{align*}42 &= 2 times 3 times 7\\\\[-0.5em]15 &= 3 times 5\\[-0.5em]6 &= 2 times 3\end{align*}\\\\ \textsf{is }42\textsf{ a multiple of }\\15\textsf{ and }6?$

Is 42 a multiple of both 15 and 6?

Yes

$A LaTex expression showing \begin{align*}105 &= 3 times 5 times 7\\\\[-0.5em]15 &= 3 times 5\\[-0.5em]35 &= 5 times 7\end{align*}\\\\ \textsf{is }105\textsf{ a multiple of }\\15\textsf{ and }35?$

Is 105 a multiple of both 15 and 35?

Yes

$A LaTex expression showing \begin{align*}105 &= 3 times 5 times 7\\\\[-0.5em]21 &= 3 times 7\\[-0.5em]15 &= 3 times 5\end{align*}\\\\ \textsf{is }105\textsf{ a multiple of }\\21\textsf{ and }15?$

Is 105 a multiple of both 21 and 15?

Yes

$A LaTex expression showing \begin{align*}63 &= 3 to the power of 2 times 7\\\\[-0.5em]9 &= 3 to the power of 2 \\[-0.5em]21 &= 3 times 7\end{align*}\\\\ \textsf{is }63\textsf{ a multiple of }\\9\textsf{ and }21?$

Is 63 a multiple of both 9 and 21?

Yes

$A LaTex expression showing \begin{align*}147 &= 3 times 7 to the power of 2 \\\\[-0.5em]15 &= 3 times 5\\[-0.5em]49 &= 7 to the power of 2 \end{align*}\\\\ \textsf{is }147\textsf{ a multiple of }\\15\textsf{ and }49?$

Is 147 a multiple of both 15 and 49?

Yes

$A LaTex expression showing \begin{align*}105 &= 3 times 5 times 7\\\\[-0.5em]35 &= 5 times 7\\[-0.5em]21 &= 3 times 7\end{align*}\\\\ \textsf{is }105\textsf{ a multiple of }\\35\textsf{ and }21?$

Is 105 a multiple of both 35 and 21?

Yes

$A LaTex expression showing \begin{align*}28 &= 2 to the power of 2 times 7\\\\[-0.5em]4 &= 2 to the power of 2 \\[-0.5em]14 &= 2 times 7\end{align*}\\\\ \textsf{is }28\textsf{ a multiple of }\\4\textsf{ and }14?$

Is 28 a multiple of both 4 and 14?

Yes