Question

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

c.

a. 450

b. 420

c. 350

d. 320

Answer 1

320................................

Answer 2

Answer:

In 450 ways 3240 ca written as product of three positive integers a , b and c.

Step-by-step explanation:

Given Number is 3240

We need to find the number of ways in which given is expressed as product of three positive integers a, b and c.

Prime factorization of 3240 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 5 = $2^3\times3^4\times5^1$

So, Number of ways in which 3 2's can be distributed to 3 integers a , b and c = $^{3+(3-1)}C_{3-1}=^5C_2=10$

Number of ways in which 4 3's can be distributed to 3 integers a , b and c = $^{4+(3-1)}C_{3-1}=^6C_2=15$

Number of ways in which 1 5's can be distributed to 3 integers a , b and c = $^{1+(3-1)}C_{3-1}=^3C_2=3$

Therefore, total number of ways = 10 × 15 × 3 = 450 ways.

Therefore, In 450 ways 3240 ca written as product of three positive integers a , b and c.