Factor Calculator
Enter a positive integer to see every factor and the prime factorization. The limit is 10,000,000 so the list stays quick.
How it works
A factor of n is a positive integer that divides n with no remainder. They come in pairs: if 3 divides 12, so does 12 ÷ 3 = 4. Walking i from 1 to √n collects each pair once.
Prime factorization writes n as a product of primes: 12 = 2² × 3. 1 has a single factor and no prime factors. 0 and negatives are excluded — “factors of −12” usually means the factors of 12.
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
Useful notes
- This lists positive factors only.
- GCF of several numbers is a different question — use the GCF calculator.
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.
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