Permutations and Combinations

To find the number of ways in which the number 831600 can be divided into two factors that are relatively prime, we start by determining the prime factorization of 831600 :
M=831600=24×33×52×7×11
The number of different prime factors is 5:2,3,5,7,11.
When dividing a number into two relatively prime factors, each prime factor must entirely go to one factor or the other. The general formula to calculate the number of ways to partition these prime factors into two groups is given by:
2n−1
where n represents the number of distinct prime factors. Thus, for 831600 :
25−1=24=16
Therefore, there are 16 different ways to split 831600 into two factors that are relatively prime.