Question
There are three natural numbers which are pairwise
co-prime. The product of the first two numbers is 105 and the product of the last two numbers is 255. If the sum of the smallest and the largest of these three numbers is denoted by 'p', then find the number of factors of 'p'.Solution
ATQ, Let the three numbers be 'a', 'b' and 'c'. According to the question, ab = 105 and bc = 255 Now, b = HCF of (105 and 255) Therefore, b = 15 And, a = (105 / 15) = 7 And, c = (255 / 15) = 17 The three numbers are 7, 15 and 17. Least number = 7 and greatest number = 17 Therefore, 'p' = 7 + 17 = 24 Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24 i.e. total 8 factors
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