2020 · Q2
The number of (a, b, c), where a, b, c are positive integers such that abc = 30, is
Elementary MathematicsNumber System
- A30
- B27
- C9
- D8
Explanation
Write 30 = 2*3*5. Each prime's single power can be assigned independently to a, b or c - 3 choices per prime. The assignments for the three distinct primes are independent, giving 3*3*3 = 27 ordered triples (a, b, c). Hence option (B).