Question : If $a^3b=abc=180;\ a, b$, and $c$ are positive integers, then the value of $c$ is:
Option 1: 110
Option 2: 1
Option 3: 4
Option 4: 25
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Correct Answer: 1
Solution :
Given: $a^3b=abc=180;\ a, b$ and $c$ are positive integers.
The factors of $180 = 2 × 2 × 3 × 3 × 5$
Since $a^3b$ contains the cube of $a$. So, $a =1$ is the only possibility.
Also $a^3b=abc$ ⇒ $a^2=c$
So, $c=1$
Hence, the correct answer is $1$.
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