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Grade: 12
        The number of triplets of positive integers {a,b,c} such that a*b*c = 2310
10 months ago

Answers : (1)

Arun
14891 Points
							
Dear shubham
2310 = 2 X 3 X 5 X 7 X 11

A non-trivial factor is a factor other than 1.

If there is only one non-trivial factor, then the triplet is (1,1,2310)

If there is one trivial factor, then we are looking for ways to factorise 2310 into two factors

If no trivial factor, then 2310 is to be factorised into three factors.

i.e. the numbers 2,3,5,7,11 are to be divided into two and three groups respectively. Here the concept of Stirling numbers of the second kind comes into play. Check out http://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind

Hence, the number of triplets is 1+ S(5,2)+S(5,3) = 41

9 months ago
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