Question
The HCF of two numbers is 12. If their product is 1728,
then how many such pairs exist?Solution
Let the two numbers be '12a' and '12b', where 'a' and 'b' are co-prime. ATQ; 12a × 12b = 1728 So, 144ab = 1728 ab = 12 Now, ab = 12 can be written as: 12 = 1 × 12 or 3 × 4 Since, only co-prime pairs are valid: (1, 12) and (3, 4) Hence, only two pairs exist.
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