Factor Calculator
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What Counts as a Factor
A factor (or divisor) of a positive integer n is any positive integer that divides n evenly, leaving no remainder. This calculator finds every factor by testing divisibility up to the square root of n: whenever a number i divides n evenly, both i and its complementary pair n / i are factors. Checking only up to the square root (rather than all the way up to n) is what keeps this fast even for large numbers, since factors always arrive in matching pairs that straddle the square root.
Factors vs. Prime Factors
This calculator lists all factors of a number, including 1 and the number itself — for example, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. That's different from prime factorization, which breaks a number down into only its prime building blocks (24 = 2 x 2 x 2 x 3). If you need that breakdown instead, use the prime factorization calculator. If you're comparing the factors of two or more numbers to find what they share, the GCF calculator is the right tool.
A Common Misconception
It's easy to assume a number has a set, "obvious" number of factors, but the count is surprisingly uneven: prime numbers always have exactly two factors (1 and themselves), while highly composite numbers like 24 or 36 can have a dozen or more. Perfect squares are the one case where a factor pairs with itself (for example, 6 x 6 = 36), which is why a perfect square always has an odd total number of factors while every other number has an even count.
Frequently Asked Questions
What is the difference between a factor calculator and a prime factorization calculator?
A factor calculator lists every positive integer that divides your number evenly, including 1 and the number itself (e.g. 24 has factors 1, 2, 3, 4, 6, 8, 12, 24). A prime factorization calculator instead breaks the number down into only its prime building blocks (24 = 2 x 2 x 2 x 3). Use this tool when you need the full list of divisors; use the prime factorization calculator when you need the prime decomposition.
How can I tell if a number is prime just from its factor list?
A number is prime if and only if it has exactly two factors: 1 and itself. If the factor list this calculator produces has more than two entries, the number is composite. The one exception is the number 1, which has only one factor and is classified as neither prime nor composite by mathematical convention.