In how many possible ways can write 3240 as a product of 3 positive integers a,b and c
Answers
Answer:
450
Step-by-step explanation:
3240 = 2 * 2 * 2 * 3 * 3 * 3 * 3 * 5
3240 = 2³ * 3⁴ * 5¹
3240 = a * b * c
Each integer Would have powers of 2 , 3 & 5
power for 2 can vary from 0 to 3
power for 3 can vary from 0 to 4
power for 5 can vary from 0 to 1
The factor 2 can be split among 3 integers in 10 different ways: (in terms of Power)
0,0,3
0,1,2
0,2,1
0,3,0
1,0,2
1,1,1
1,2,0
2,0,1
2,1,0
3,0,0
The factor 3 can be split among 3 integers in 15 different ways: (in terms of Power)
0,0,4
0,1,3
0,2,2
0,3,1
0,4,0
1,0,3
1,1,2
1,2,1
1,3,0
2,0,2
2,1,1
2,2,0
3,0,1
3,1,0
4,0,0
The factor 5 can be split among 3 integers in 3 different ways: (in terms of Power)
0,0,1
0,1,0
1,0,0
Total Combination = 10*15*3 = 450
Answer:
450
Step-by-step explanation:
The number 3240 can be factorized as 2 power 3
3 power 4
5 power 1
The formula for finding the number of ways
n-r-1 C r-1
Applying for each term we get ,
2 power 3 ------> 3 + 3 - 1 C 3-1 ----> 5 C 2 = 10
3 power 4 ------> 4 + 3 -1 C 3-1 ----> 6 C 2 = 15
5 power 1 -------> 1 + 3 - 1 C 3-1 -----> 3 C 2 = 3