Factor Calculator
List every positive divisor of one integer and write its prime factorization — homework factor trees, not the GCF of a whole list.
How to use
- Enter a positive integer up to 10,000,000.
- Read the factor list, how many there are, and the prime factorization.
- A prime such as 13 shows only 1 and 13.
- Use GCF when you have two or more numbers to compare, or LCM for a shared multiple.
How it works
A factor of n divides n with no remainder. They come in pairs: 3 divides 12, so does 4. Walking from 1 to √n finds each pair once. 12 has 1, 2, 3, 4, 6, 12. A prime has exactly two: 1 and itself.
Prime factorization writes n as primes: 12 = 2² × 3. 100 = 2² × 5². 1 has a factor list {1} and no prime product. 0 and negatives are out of scope; “factors of −12” usually means the factors of 12.
The 10 million cap keeps the walk instant in the browser. Larger integers belong in a computer-algebra system.
This is one number. The greatest common factor of 12 and 18 is 6 — that needs two inputs on the GCF page. Simplifying a fraction still starts here or there, depending on whether you want the full list or just the shared piece.
A square such as 36 has an odd count of factors because 6 pairs with itself. Perfect squares are the usual “why is there a middle factor?” case. Powers of two (8, 16, 32) have only 2 as a prime, so the list is 1, 2, 4, …, n.
Formula
If i divides n, then both i and n/i are factors 12 = 2² × 3 Factors of 12: 1, 2, 3, 4, 6, 12
Worked examples
A composite number
12 → 1, 2, 3, 4, 6, 12 and 2^2 × 3
A prime
13 → 1, 13
Factor lists that come up in class
| n | Factors | Prime factorization |
|---|---|---|
| 12 | 1, 2, 3, 4, 6, 12 | 2² × 3 |
| 13 | 1, 13 | 13 |
| 36 | 1, 2, 3, 4, 6, 9, 12, 18, 36 | 2² × 3² |
| 100 | 1, 2, 4, 5, 10, 20, 25, 50, 100 | 2² × 5² |
| 1 | 1 | none |
Useful notes
- Positive factors only.
- 1 is not prime; primes have exactly two factors.
- Limit 10,000,000.
FAQ
- How do I find the factors of a number?
Test integers up to the square root. Each exact divisor i gives a pair (i, n/i). For 12 the pairs are (1, 12), (2, 6) and (3, 4).
- How do I find the prime factorization?
Divide out the smallest prime as many times as it goes, then the next. 12 ÷ 2 = 6, 6 ÷ 2 = 3, and 3 is prime, so 12 = 2² × 3.
- Why is there a 10 million limit?
Listing every factor is cheap at that size and stays instant in the browser. Larger inputs belong in a computer-algebra tool.
- What are the factors of 36?
1, 2, 3, 4, 6, 9, 12, 18, 36. Prime factorization 2² × 3².
- Is 1 a prime?
No. It has only one positive factor. Prime factorization of 1 is empty.
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