Sum of all factors of 36 — Number System Aptitude Question
Sum of all factors of 36: What is the sum of all the factors of 36? Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
What is the sum of all the factors of 36?
Options
- 55
- 78
- 91
- 96
Show the answer and the worked solution
Correct answer: C. 91
Worked solution
- 36 = 2² × 3².
- Sum of factors = (1 + 2 + 4) × (1 + 3 + 9) = 7 × 13 = 91.
- Check by listing: 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 36 = 91. ✓
Answer: 91.
The idea
The sum of factors multiplies one geometric series per prime. It is worth learning alongside the count formula, because papers ask for both from the same factorisation.
Shortcut. A perfect square has an odd sum of factors, which rules out 78 and 96. 1 + 36 + 2 + 18 is already 57, past 55, leaving 91.
Common trap. 55 — the sum of the proper factors only, leaving out 36 itself (91 − 36 = 55).