Factor Calculator
Enter a whole number from 1 to 1,000,000,000,000 to see all of its positive factors in order. You also get the factor pairs, the prime factorization, how many factors there are, their sum, and whether the number is prime or composite.
Last updated November 3, 2026
A whole number from 1 to 1,000,000,000,000.
Result
36 is a composite number with 9 factors.
| Measure | Value |
|---|---|
| Type | Composite |
| Prime factorization | 2^2 x 3^2 |
| Number of factors | 9 |
| Sum of factors | 91 |
| Smaller factor | Larger factor |
|---|---|
| 1 | 36 |
| 2 | 18 |
| 3 | 12 |
| 4 | 9 |
| 6 | 6 |
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Show the work
Formula: Factors come from the prime factorization: number of factors = (a + 1)(b + 1)… for n = p^a × q^b …
- You entered 36.
- Prime factorization of 36: 2^2 x 3^2.
- Count: add 1 to each exponent and multiply: (2 + 1) × (2 + 1) = 9 factors.
- Multiply the prime powers in every combination to get the factors: 1, 2, 3, 4, 6, 9, 12, 18, 36.
- Pair each factor up to √36 with 36 ÷ that factor: 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6 (5 pairs).
- Sum: for each prime add every power of it up to its exponent, then multiply: (1 + 2 + 4) = 7 × (1 + 3 + 9) = 13 = 91.
Result: 36 is a composite number with 9 factors.
How the factors of a number are found
n = p^a × q^b × … gives (a + 1)(b + 1)… factors
A factor of n is a whole number that divides n with no remainder. Factors come in pairs that multiply to n, so only the numbers up to the square root of n need to be tested. For 36 that means checking 1 to 6, and each hit gives a pair: 1 × 36, 2 × 18, 3 × 12, 4 × 9 and 6 × 6.
The calculator works from the prime factorization instead. Once n is written as a product of prime powers, every combination of those powers is a factor. Write 36 as 2² × 3²: the exponent of 2 can be 0, 1 or 2 and the exponent of 3 can be 0, 1 or 2, giving 3 × 3 = 9 factors. In general you add 1 to each exponent and multiply.
The sum of the factors is also found per prime. Add the powers of each prime up to its exponent, then multiply the results. For 36 that is (1 + 2 + 4) × (1 + 3 + 9) = 7 × 13 = 91.
See how we calculate for the formulas, sources and review schedule behind every calculator.
Also useful alongside this calculator: Basic Calculator, Fraction Calculator and Exponent Calculator.
Prime, composite and the number 1
A prime number has exactly two factors, 1 and itself. 2, 3, 5, 7 and 97 are prime, and 2 is the only even prime. A composite number has more than two factors, such as 12 with 1, 2, 3, 4, 6 and 12.
The number 1 has only one factor, itself, so it is neither prime nor composite. This convention keeps the rule that every number above 1 has exactly one prime factorization.
A number has an odd count of factors only when it is a perfect square, because that is the one case where a factor pairs with itself. 36 has 9 factors and 6 pairs with itself, while 48 has 10.
Quick divisibility tests
A number is divisible by 2 if it ends in an even digit, by 5 if it ends in 0 or 5, and by 10 if it ends in 0. It is divisible by 3 when its digits add up to a multiple of 3, and by 9 when they add up to a multiple of 9. For 5,436 the digits add to 18, so 3 and 9 are both factors.
These tests find small prime factors quickly by hand. The calculator applies trial division by primes up to the square root of the number, which is at most 1,000,000 steps for the largest input.
Factors, multiples and perfect numbers
Factors divide a number and are never larger than it, while multiples are what you get by multiplying it and never smaller. The factors of 12 are 1, 2, 3, 4, 6 and 12, and its multiples are 12, 24, 36 and so on.
Factors that two numbers share are their common factors, and the largest is the greatest common factor. A perfect number equals the sum of its factors except itself. The factors of 6 add to 12, which is twice 6, and the factors of 28 add to 56, twice 28.
How to use the Factor Calculator
- Enter a whole number from 1 to 1,000,000,000,000.
- Read the type, the prime factorization, the number of factors and their sum.
- Scan the full factor list and the table of factor pairs.
- Open Show the work, then Copy, Print or Share the result.
Worked example
List the factors of 60. Trial division gives 60 = 2² × 3 × 5. Adding 1 to each exponent gives (2 + 1)(1 + 1)(1 + 1) = 12 factors. Combining the primes in every way gives 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60. They pair up as 1 × 60, 2 × 30, 3 × 20, 4 × 15, 5 × 12 and 6 × 10. Their sum is (1 + 2 + 4) × (1 + 3) × (1 + 5) = 7 × 4 × 6 = 168, so 60 is a composite number.
| Number | Prime factorization | Factors | Sum of factors |
|---|---|---|---|
| 12 | 2^2 x 3 | 6 | 28 |
| 36 | 2^2 x 3^2 | 9 | 91 |
| 48 | 2^4 x 3 | 10 | 124 |
| 60 | 2^2 x 3 x 5 | 12 | 168 |
| 97 | 97 | 2 | 98 |
| 100 | 2^2 x 5^2 | 9 | 217 |
| 360 | 2^3 x 3^2 x 5 | 24 | 1,170 |
Frequently asked questions
How many factors can a number have?
It depends on its primes. A prime has 2. 720,720 has 240 factors, and 1,000,000,000,000 has 169 because it equals 2^12 × 5^12 and 13 × 13 is 169.
Does the calculator handle negative numbers or decimals?
No. Factors are defined here for positive whole numbers, so 0, negative numbers and decimals show a message asking for a whole number from 1 to 1,000,000,000,000.
What is the difference between a factor and a prime factor?
A factor is any whole number that divides evenly. A prime factor is a factor that is itself prime. The factors of 12 include 4 and 6, but its prime factors are only 2 and 3.
Is my number stored anywhere?
No. The factors are computed in your browser and nothing you type is sent or saved. A shared link only carries the number in its address.