Question

what is the number of ways of expressing 3600 as a product of three ordered positive integers (abc bca etc. are counted as distinct). for example the number 12 can be expressed as a product of three ordered positive integers in 18 different ways.

Answer 1

12 in 18 ways

see we can have three cases as 12 have factors 3x4,2x6,12x1...
so case 1 - (3,4,1) Six ways as repetition can be there..
eg - (3,4,1),(3,1,4),(1,3,4),(1,4,3),(4,1,3),(4,3,1) so total Six ways..
case 2 (2,6,1) Again 6 ways
case 3 (12,1,,) again 6 ways
finally = 6+6+6 = 18
i hope it helped....