Question

In how many possible ways can you write 3240 as a product of 3 positive integers a,b and c

Answer 1

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