Question:
If $a$, $b$, $c$ are different integers such that $(a,b) = c$, which of the following statements is true?
If $a$, $b$, $c$ are different integers such that $(a,b) = c$, which of the following statements is true?
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The GCD of two integers divides both of them — this is the defining property of the greatest common divisor.
Updated On: May 2, 2026
- $c \mid a$
- $c \mid b$
- $b \mid a$
- None of these
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Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
$(a,b) = c$ means $c$ is the greatest common divisor of $a$ and $b$.
Step 2: Detailed Explanation:
By definition of GCD, $c$ divides both $a$ and $b$. So both $\dfrac{a}{c}$ and $\dfrac{b}{c}$ are integers, i.e.\ $c \mid a$ and $c \mid b$.
Option (A) $c \mid a$ is therefore correct.
Step 3: Final Answer:
$c \mid a$ is true.
$(a,b) = c$ means $c$ is the greatest common divisor of $a$ and $b$.
Step 2: Detailed Explanation:
By definition of GCD, $c$ divides both $a$ and $b$. So both $\dfrac{a}{c}$ and $\dfrac{b}{c}$ are integers, i.e.\ $c \mid a$ and $c \mid b$.
Option (A) $c \mid a$ is therefore correct.
Step 3: Final Answer:
$c \mid a$ is true.
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