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Product of two numbers is 16184 and their HCF is 17, then how many possible pairs of numbers are there which will satisfy the given conditions.

Product of two numbers is 16184 and their HCF is 17, then how many possible pairs of numbers are there which will satisfy the given conditions. Correct Answer 2 pairs

Given:

Product of two numbers = 16184

HCF = 17

Concept used:

if HCF of two numbers is p then the numbers are of type pk1 and pk2, where k1 and k2 are co-prime numbers

Calculation:

Let the numbers be 17x and 17y

Product of numbers = 17x × 17y

⇒ 16184 = 289xy

⇒ xy = 16184/289

⇒ xy = 56

Here x and y are co-prime numbers

Possible values of x and y are

1 and 56

7 and 8

∴ There are 2 pair of numbers

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