Count the Factors of a Number
Count all factors of a number from its prime factorisation.
Factor count = product of (each prime power + 1)
1How it works
Write the number as a product of prime powers. Add 1 to each power and multiply those results — that is the total number of factors.
2How to apply (in seconds)
- Prime factorise the number (e.g. 72 = 2³ × 3²).
- Add 1 to each power (3+1 and 2+1).
- Multiply the results: 4 × 3.
3Worked examples
Example 1 Worked solution
Q. How many factors does 72 have?
- 72 = 2³ × 3².
- (3+1)(2+1) = 4 × 3.
✓ 12 factors
4When to use it
- ✦Number-system MCQs about factors and divisors.
5Cautions & tips
- !For even or odd factors only, split off the power of 2 first.