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Prime Factorization - Is Integer a Factor of Both - From Values as Factors (Level 3)

This math topic focuses on advanced factoring skills and the determination of common factors in different numbers. It employs prime factorization to assess whether a given integer is a factor of two other numbers. Problems present equations involving exponentiation and multiplication of prime numbers, requiring students to decide if one number is a factor of the others listed. Each question is structured with two potential answers: "Yes" or "No." This analysis aids students in understanding factor relationships and the concept of the greatest common factor at a deeper level.

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

Is Integer a Factor of Both - From Values as Factors

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Is 735 a factor of both 1470 and 8085?

735=x⋅d⋅r21470=2⋅3⋅5⋅728085=3⋅5⋅72⋅11is 735 a factor of1470 and 8085?\begin{align*}735 &= x \cdot d \cdot r^2\\[-0.5em]1470 &= 2 \cdot 3 \cdot 5 \cdot 7^2\\[-0.5em]8085 &= 3 \cdot 5 \cdot 7^2 \cdot 11\end{align*}\\\\ \textsf{is }735\textsf{ a factor of}\\1470\textsf{ and }8085?