Question : The product of the two numbers is 1500 and their HCF is 10. The number of such possible pairs is/are:
Option 1: 1
Option 2: 3
Option 3: 4
Option 4: 2
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Correct Answer: 2
Solution :
Given: The product of the two numbers is 1500 and their HCF is 10.
Let the two numbers be $10x$ and $10y$
So, $10x×10y=1500$
⇒ $100xy=1500$
⇒ $xy=15$
Now, 15 = 15 × 1 and 15 = 3 × 5
Therefore, the possible number of pairs which are co-prime to each other is 2.
Hence, the correct answer is 2.
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