Question

In how many possible ways can you write 1800 as a product of 3 positive integers a b and c

Answer 1

Answer:

360

Step-by-step explanation:

Given  

In how many possible ways can you write 1800 as a product of 3 positive integers a b and c

Now we know that

(n + r – 1) C(r – 1) where n = power and r = number of integers.

So factors of 1800 = 2 x 2 x 2 x 3 x 3 x 5 x 5 = 2^3 x 3^2 x 5^2

Substituting we get

1. (3 + 3 – 1)C(3 -1) = 5C2 = 5! / 2!(5 -  2)! = 10

2. (2 + 3 – 1)C(3 – 1) = 4C2 = 4! / 2!(4 – 2)! = 6

3. (2 + 3 – 1)C(3 – 1) = 4C2 = 6

So multiplying we get 10 x 6 x 6 = 360

So we can write in 360 possible ways