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    Question

    The HCF of two numbers is 18. If their product is 5832,

    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 '18a' and '18b', where 'a' and 'b' are co-prime. ATQ; 18a × 18b = 5832 So, 324ab = 5832 ab = 18 Now, ab = 18 can be written as: 18 = 1 × 18 or 2 × 9 or 3 × 6 Since, only co-prime pairs are valid: (1, 18) and (2, 9) (3, 6) is not considered as they are not co-prime. Hence, only two pairs exist.

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