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.

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Is Integer a Factor of Both - From Values as Factors

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Is 315 a factor of both 2310 and 1638?

315=c2px2310=2357111638=232713is 315 a factor of2310 and 1638?\begin{align*}315 &= c^2 \cdot p \cdot x\\\\[-0.5em]2310 &= 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11\\[-0.5em]1638 &= 2 \cdot 3^2 \cdot 7 \cdot 13\end{align*}\\\\ \textsf{is }315\textsf{ a factor of}\\2310\textsf{ and }1638?

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