Question
The HCF of two numbers is 20. If their product is
16000, then how many such pairs exist?Solution
Let the two numbers be '20a' and '20b', where 'a' and 'b' are co-prime. ATQ; 20a × 20b = 16000 So, 400ab = 16000 ab = 40 Now, ab = 40 can be written as: 40 = 1 × 40 or 5 × 8 Since, only co-prime pairs are valid: (1, 40) and (5, 8) Hence, only two pairs exist.
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