Counting the divisors of 360 — Aptitude Question
Counting the divisors of 360: How many positive divisors does 360 have? Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
How many positive divisors does 360 have?
Options
- 18
- 20
- 24
- 30
Show the answer and the worked solution
Correct answer: C. 24
Worked solution
- 360 = 2³ × 3² × 5¹.
- Number of divisors = (3 + 1)(2 + 1)(1 + 1) = 4 × 3 × 2 = 24.
Answer: 24.
The idea
Every divisor picks an exponent for each prime from 0 up to its power, so multiply (exponent + 1) across the primes. The same factorisation also gives the sum of divisors and the number of odd or even divisors.
Shortcut. √360 ≈ 19, and the divisors below it — 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18 — number 12. Each pairs with one above, so 24.
Common trap. 18 — the count for 2² × 3² × 5 = 180, from dropping one factor of 2 when factorising 360.