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    Question

    Aman is forming pairs of two natural numbers, A and B,

    such that their product equals 350. He wants to determine how many such pairs exist where A and B are co-prime. How many such pairs can be created?  
    A 6 Correct Answer Incorrect Answer
    B 2 Correct Answer Incorrect Answer
    C 5 Correct Answer Incorrect Answer
    D 4 Correct Answer Incorrect Answer

    Solution

    Co-prime numbers are the ones whose HCF is 1. The possible number of pairs of ‘A’ and ‘B’, such that, ‘A’ and ‘B’ are co-prime = 2k – 1 Where, ‘k’ is the number of prime factors of the product. 350 = 21 × 52 × 71 So, the number of prime factors of 350 = k = 3 So, the possible number of pairs of ‘A’ and ‘B’, such that they are co-prime = 23 – 1 = 22 = 4

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