The product of the two numbers is 1500 and their HCF is 10 The number of such possible pairs is are ........

Quantitative Aptitude (CGL) LCM, HCF

The product of the two numbers is 1500 and their HCF is 10. The number of such possible pairs is/are:

This questions was previously asked in

SSC CGL Tier II Paper 1 (02.03.2023)

To find the number of possible pairs of numbers that have a product of 1500 and an HCF of 10, consider the following:

- Let the numbers be 10a and 10b, where a and b are coprime integers (since HCF is 10).

- Thus, 10a * 10b = 1500 implies a * b = 15.

- The possible coprime pairs (a, b) from the factors of 15 are (1, 15) and (3, 5).

So, there are 2 pairs of numbers: (10, 150) and (30, 50).

- Option:4 - 2 is the correct answer as there are two possible pairs.

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