Even factors of 1440 — Number System Aptitude Question
Even factors of 1440: How many even factors does 1440 have? Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
How many even factors does 1440 have?
Options
- 18
- 24
- 30
- 36
Show the answer and the worked solution
Correct answer: C. 30
Worked solution
- 1440 = 2⁵ × 3² × 5.
- An even factor is 2 × (a factor of 2⁴ × 3² × 5).
- That count is (4 + 1)(2 + 1)(1 + 1) = 5 × 3 × 2 = 30.
- Check: total factors = 6 × 3 × 2 = 36, of which 6 are odd, leaving 30 even. ✓
Answer: 30.
The idea
Even factors = total factors − odd factors, and the odd ones are the factors of the number with all its 2s removed. Both routes agree; the second is faster when the power of 2 is large.
Shortcut. With 2⁵ in the factorisation, a factor's power of 2 can be 0 to 5, and five of those six choices make it even: 5/6 of the 36 factors = 30.
Common trap. 36 — the total number of factors of 1440, forgetting to remove the 6 odd ones (the factors of 45).