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    Question

    The HCF of two numbers is 20. If their product is

    16000, then how many such pairs exist?
    A 3 Correct Answer Incorrect Answer
    B 2 Correct Answer Incorrect Answer
    C 1 Correct Answer Incorrect Answer

    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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