Question
The HCF of two numbers is 15. If their product is 3375,
then how many such pairs exist?Solution
Let the two numbers be '15a' and '15b', where 'a' and 'b' are co-prime. ATQ; 15a × 15b = 3375 So, 225ab = 3375 ab = 15 Now, ab = 15 can be written as: 15 = 1 × 15 or 3 × 5 Since, only co-prime pairs are valid: (1, 15) and (3, 5) Hence, only two pairs exist.
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