Question

The number of (a,b,c), where a,b,c are positive integers such that abc = 30, is 
1. 30
2. 27
3. 9
4. 8

Answer 1

Correct Answer - Option 2 : 27

Given :

There are 3 number a, b and c where abc = 30.

Calculations :

All divisors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30. 

Selecting any 3 numbers from all divisors so that we get multiplication as 30 

1) 1 × 1 × 30 = 30 

Number of ways to arrange 1, 1 and 30 = 3!/2 = 3 

2) 1 × 3 × 10 = 30 

Number of ways to arrange 1, 3 and 10 = 3! = 6 

3) 2 × 3 × 5 = 30 

Number of ways to arrange 2, 3 and 5 = 3! = 6

4) 1 × 5 × 6 = 30 

Number of ways to arrange 1, 5 and 6 = 3! = 6 

5) 1 × 2 × 15 = 30 

Number of ways to arrange 1, 2 and 15 = 3! = 6   

Total solutions = 6 + 6 + 6 + 6 + 3

⇒ 27 ways 

∴ Option 2 will be the correct choice.