Question
The HCF of two numbers is 18. If their product is 5832,
then how many such pairs exist?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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IMITATION
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