Total factors of 4200 — Number System Aptitude Question
Total factors of 4200: How many factors does 4200 have? Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
How many factors does 4200 have?
Options
- 36
- 42
- 48
- 56
Show the answer and the worked solution
Correct answer: C. 48
Worked solution
- 4200 = 2³ × 3¹ × 5² × 7¹.
- Number of factors = (3 + 1)(1 + 1)(2 + 1)(1 + 1) = 4 × 2 × 3 × 2 = 48.
Answer: 48.
The idea
Each factor chooses an exponent from 0 up to the power available, so multiply (exponent + 1) over all primes. Forgetting a prime with exponent 1 halves the count.
Shortcut. Write 4200 = 7 × 600. 600 = 2³ × 3 × 5² has 4 × 2 × 3 = 24 factors, and the coprime 7 doubles the count to 48.
Common trap. 36 — the count for 2² × 3 × 5² × 7 = 2100, from dropping one factor of 2 in the factorisation.