A factor calculator finds every positive integer that divides a given number exactly with no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. This calculator also shows factor pairs, prime factorization, the number of positive factors, and whether the number is prime or composite.
What Is a Factor?
A factor, also called a divisor, is an integer that divides another integer exactly. If dividing a number n by d leaves no remainder, then d is a factor of n.
or equivalently
n = d × q
For example, 4 is a factor of 20 because 20 ÷ 4 = 5 with no remainder. By contrast, 6 is not a factor of 20 because 20 ÷ 6 leaves a remainder.
How to Find Factors of a Number
- Start with 1.
- Test possible divisors up to the square root of the number.
- If the number divides evenly, record the divisor.
- Also record its matching quotient as the paired factor.
- Remove duplicates when the number is a perfect square.
- Sort the factors from smallest to largest.
You only need to test divisors up to √n because factors occur in pairs. If one factor is greater than √n, its matching factor must be smaller than √n.
Factor Pairs
A factor pair is a pair of integers whose product equals the original number. For 36, the positive factor pairs are:
1 × 36 = 36
2 × 18 = 36
3 × 12 = 36
4 × 9 = 36
6 × 6 = 36
Factor pairs make it easier to verify that no factors are missing.
Prime Factors and Prime Factorization
A prime factor is a factor that is also a prime number. Prime factorization writes a positive integer as a product of prime numbers.
The calculator above shows prime factorization automatically. This is useful when working with divisibility, GCF, LCM, fractions, and other number-theory problems.
Factor Examples
Example 1: Factors of 36
Factor pairs:
1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6
All positive factors:
1, 2, 3, 4, 6, 9, 12, 18, 36
Prime factorization:
36 = 22 × 32
Number type: Composite and perfect square
Example 2: Factors of 17
17 is divisible evenly only by 1 and 17.
Factors: 1, 17
Prime factorization: 17
Number type: Prime
Factors vs Multiples
Factors and multiples are related, but they are not the same thing.
| Concept | Meaning | Example Using 6 |
|---|---|---|
| Factors | Numbers that divide 6 exactly | 1, 2, 3, 6 |
| Multiples | Numbers produced by multiplying 6 by integers | 6, 12, 18, 24, 30... |
Common Factor Mistakes
1. Forgetting 1 and the number itself
Every positive integer has at least 1 and itself as factors.
2. Confusing factors with multiples
Factors divide a number exactly. Multiples are created by multiplying the number by integers.
3. Missing the paired factor
If 3 divides 24, then 8 is also a factor because 3 × 8 = 24.
4. Entering decimals
This calculator is for integer factors, so values such as 12.5 are rejected rather than silently rounded or truncated.
5. Confusing all factors with prime factors
The factors of 12 are 1, 2, 3, 4, 6, and 12, while its prime factorization is 22 × 3.
How to Verify the Factors
Multiply each factor pair to confirm that it gives the original number. For example, 4 × 9 = 36 and 3 × 12 = 36.
You can also divide the original number by any listed factor. A correct factor produces an integer quotient with no remainder.
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How This Calculator Works
The calculator checks possible divisors only up to the square root of the entered integer. Whenever a divisor divides evenly, both the divisor and its matching quotient are recorded. The results are then deduplicated and sorted from smallest to largest.
Prime factorization is calculated separately using repeated division by prime candidates. The tool also counts the positive factors and classifies the number as prime or composite.
Prepared by the Utilixea Editorial Team.
Last updated: July 21, 2026.
Factor Calculator FAQs
A factor is an integer that divides another integer exactly without leaving a remainder.
Factor pairs are two integers whose product equals the original number. For 24, examples include 1 × 24, 2 × 12, 3 × 8, and 4 × 6.
Factors divide a number exactly, while multiples are produced by multiplying the number by integers.
Prime factors are prime numbers whose product equals the original number. For example, 20 = 2 × 2 × 5 = 2² × 5.
Yes. Every positive integer is divisible by 1, so 1 is always one of its positive factors.
Yes. Integers can have negative factor pairs as well, but this calculator focuses on the positive factors most commonly used in school-level factor problems.
A positive integer greater than 1 is prime when its only positive factors are 1 and the number itself.
Factors occur in pairs. If one factor is greater than the square root of the number, its matching factor must be smaller than the square root, so every pair is found once you reach √n.
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