0 votes 0 votes a)if 32400 = 1* 32400 = 2*16200 = 3*10800 = ....................(n times) what is the max value of n A_i_$_h asked Sep 12, 2017 A_i_$_h 602 views answer comment Share Follow See all 7 Comments See all 7 7 Comments reply Rishabh Gupta 2 commented Sep 12, 2017 reply Follow Share 6. Since 1, 2, 3, 4, 5, 6 are all factors of 32400. But 7 is not. Which breaks the streak. 0 votes 0 votes A_i_$_h commented Sep 12, 2017 reply Follow Share what if 7 is skipped and from 8 its considered? what if it was .....what it is the total number of ways it can be split as a multiplication of two numbers 1 votes 1 votes Rishabh Gupta 2 commented Sep 12, 2017 reply Follow Share oh Sorry. I misinterpreted the question. In that case, I think it should be 38. Because prime factorization of 32400 = $2^43^45^2$. From which we can form a total of 5 x 5 x 3 = 75 factors of 32400. Out of these half will be repeated like this: 2*16200, ... 16200*2. So we get 38. :) Am I right?? 0 votes 0 votes prateekdwv commented Sep 12, 2017 reply Follow Share Here is my approach to the questions you just asked in your comment. First, find the prime factorization of the number $32400 = 2^4*3^4*5^2$. Now count the number of factors of $32400$ using this factorization. That will be, $5*5*3=75$. This number includes redundant multiplication of type $1*32400 = 32400*1$, $2*16200=16200*2$ etc.. That can be dealt by halving the number of factor - $\left \lceil 75/2 \right \rceil = 38$ 1 votes 1 votes A_i_$_h commented Sep 12, 2017 reply Follow Share so the answer to tha main question would be 6 or 38?? 0 votes 0 votes Rishabh Gupta 2 commented Sep 12, 2017 reply Follow Share 38. According to your comment "what it is the total number of ways it can be split as a multiplication of two numbers". 0 votes 0 votes A_i_$_h commented Sep 12, 2017 reply Follow Share okay :) 0 votes 0 votes Please log in or register to add a comment.