Problem Solving

ronnie1985 wrote:I want to know:What is the formula for calculating the number of distinct pairs of factors for a given number.

Number of distinct pairs of factors for a given integer = (Number of distinct factors of the integer)/2

And if the integer is a square of an integer then, number of distinct pairs of factors the integer = (Number of distinct factors of the integer + 1)/2

Now, number of factors of an integer whose prime factorization is of the form (p^a)*(q^b)*(r^c)... is (a + 1)(b + 1)(c + 1)...

Now coming to the question, let's check each of the options..

• (A) 4 = (2^2) --> Number of factors = (2 + 1) = 3 --> Number of pairs = (3 + 1)/2 = 2
  (B) 20 = (2^2)*(5^1) --> Number of factors = (2 + 1)*(1 + 1) = 6 --> Number of pairs = 6/2 = 3
  (C) 30 = (2^1)*(3^1)*(5^1) --> Number of factors = (1 + 1)*(1 + 1)*(1 + 1) = 8 --> Number of pairs = 8/2 = 4 ---> ANSWER
  (D) 60 --> No need to calculate
  (E) 80 --> No need to calculate

The correct answer is C.