Question
The HCF of two numbers is 14. If their product is 5488,
then how many such pairs exist?Solution
Let the two numbers be '14a' and '14b', where 'a' and 'b' are co-prime. ATQ; 14a × 14b = 5488 So, 196ab = 5488 ab = 28 Now, ab = 28 can be written as: 28 = 1 × 28 or 4 × 7 Since, only co-prime pairs are valid: (1, 28) and (4, 7) Hence, only two pairs exist.
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