Factors Calculator
The factors of a number are the whole numbers that divide it exactly. Listing them helps you simplify fractions, find common factors and recognise special numbers. Enter a number to get every factor and factor pair, the count and the sum, plus a classification: prime, perfect, abundant or deficient.
How to use the factors calculator
- Enter a whole number from 1 to 1,000,000,000.
- Read the list of factors and the factor pairs.
- Check the classification: it compares the sum of the proper divisors with the number itself.
Formula
Test every whole number from 1 up to √n. Each divisor d you find gives a pair (d, n ÷ d). A number is perfect if its proper divisors (all factors except itself) add up to the number, abundant if they add up to more and deficient if to less.
Worked examples
A perfect number
28 has factors 1, 2, 4, 7, 14 and 28. The proper divisors add up to 1 + 2 + 4 + 7 + 14 = 28, so it is perfect.
An abundant number
12 has proper divisors 1, 2, 3, 4 and 6, which add up to 16, more than 12. So 12 is abundant.
A perfect square
36 has an odd number of factors (9) because 6 × 6 pairs with itself.
Special kinds of number
| Type | Definition | Examples |
|---|---|---|
| Prime | Exactly two factors | 2, 3, 5, 7, 11 |
| Composite | More than two factors | 4, 6, 8, 9, 10 |
| Perfect | Proper divisors sum to the number | 6, 28, 496 |
| Abundant | Proper divisors sum to more | 12, 18, 20, 24 |
| Deficient | Proper divisors sum to less | Every prime, 8, 9, 10 |
Factor pairs and squares
Factors come in pairs that multiply to the number: 28 = 1 × 28 = 2 × 14 = 4 × 7. If a pair repeats (6 × 6 = 36) the number is a perfect square, which is why perfect squares have an odd number of factors.
Use them to simplify
To simplify 28/42, list the factors of each: the greatest common one is 14, so 28/42 = 2/3. For bigger numbers, use the GCF calculator.
Ancient curiosity
Euclid described a rule for building even perfect numbers more than 2,000 years ago. Whether an odd perfect number exists is still an open question.
Practice problems
Try these yourself first, then check your answer. The answers come from the calculator above.
- List the factors of 48.
Show answer
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Is 100 abundant, perfect or deficient?
Show answer
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
Common mistakes to avoid
- Forgetting that 1 and the number itself are always factors.
- Confusing factors with multiples. Factors divide the number; multiples are what it divides into.
- Stopping the search early. You only need to test up to √n, but you must include the partner of each divisor.
Frequently asked questions
What are factors?
Numbers that divide another number exactly, with no remainder.
What is a perfect number?
A number equal to the sum of its proper divisors. 6, 28 and 496 are perfect.
Why do perfect squares have an odd number of factors?
One factor, the square root, pairs with itself, so the total is odd.
How do factors relate to prime factorization?
You can build every factor by multiplying together some of the prime factors. See the prime factorization calculator.
Reviewed September 26, 2026 by the SolveCalcPro editorial team. Found a mistake? Tell us; see our editorial policy.