Math
Factor Calculator
Enter a whole number to list every factor from 1 to the number itself, grouped into factor pairs that multiply to it.
The calculator also gives the prime factorization, counts the divisors with the exponent formula, adds them up, and classifies the number as prime, perfect, abundant, or deficient. Numbers up to one trillion are handled exactly.
A positive whole number up to 1,000,000,000,000.
Try an example
Result
All factors
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- Number of factors
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- Factor pairs
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- Prime factorization
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- Sum of factors
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- Classification
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Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the factor calculator solves
Enter a whole number to list every factor from 1 to the number itself, grouped into factor pairs that multiply to it. The calculator also gives the A whole number above 1 whose only factors are 1 and itself. factorization, counts the divisors with the The small raised number saying how many times to multiply the base by itself. formula, adds them up, and classifies the number as prime, perfect, abundant, or deficient. Numbers up to one trillion are handled exactly.
Formula
How to use it
- Enter a positive whole number.
- Read the full factor list and the factor pairs that multiply to your number.
- Use the prime factorization, divisor count, and divisor sum in the steps to see why the list is complete.
How to read the answer
Factors come in pairs that multiply to the number, so you only need to search up to its square root. A perfect square has an odd number of factors because its square root pairs with itself. The sum of the proper factors (everything except the number itself) decides the classification: equal means perfect, more means abundant, less means deficient.
Common mistakes and edge cases
- Forgetting 1 and the number itself; both are always factors.
- Confusing factors with multiples: factors of 12 are 1, 2, 3, 4, 6, 12; multiples are 12, 24, 36, ….
- Listing only prime factors when the question asks for all factors.
- Stopping the search before √n, or continuing past it and double-counting.
- Counting a repeated pair twice for perfect squares: 6 × 6 gives one factor, 6.
Worked examples
Factors of 36
Nine factors; 36 is a perfect square.
All factors
1, 2, 3, 4, 6, 9, 12, 18, 36
Perfect number 28
1 + 2 + 4 + 7 + 14 = 28.
All factors
1, 2, 4, 7, 14, 28
Prime number 97
Only 1 and 97.
All factors
1, 97
Highly composite 360
24 factors.
All factors
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
The number 1
A single factor.
All factors
1
Large number 1,000,000,007
A large prime.
All factors
1, 1,000,000,007
Zero
Not allowed: every number divides 0.
All factors
Error
Frequently asked questions
What are the factors of 36?+
1, 2, 3, 4, 6, 9, 12, 18, and 36. The factor pairs are 1 × 36, 2 × 18, 3 × 12, 4 × 9, and 6 × 6.
How do I find all the factors of a number quickly?+
Test divisors from 1 up to the square root. Each divisor d you find gives a second one, n ÷ d. For 36 you only test 1 through 6.
How many factors does a number have?+
Add 1 to each exponent in the prime factorization and multiply. 360 = 2³ × 3² × 5 has (3 + 1)(2 + 1)(1 + 1) = 24 factors.
What is a perfect number?+
A number equal to the sum of its proper factors. 28 = 1 + 2 + 4 + 7 + 14. The next ones are 496 and 8128.
What is the difference between factors and prime factors?+
Factors are every whole number that divides evenly; prime factors are only the primes among them. The prime factors of 36 are 2 and 3, written 2² × 3².
Why do perfect squares have an odd number of factors?+
Factors pair up as d and n ÷ d, but for a square the root pairs with itself, so one factor is counted once and the total is odd.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026