Factor Calculator
Find every positive divisor of a whole number and instantly see if it is prime.
Example
For n = 28, loop i from 1 to 5 (since 5² ≤ 28 < 6²):
1 × 28 2 × 14 4 × 7
Factors: 1, 2, 4, 7, 14, 28
Count: 6 Sum: 56 Prime: No
Since 28 has 6 factors (not exactly two), it is not prime.
How it works
Enter a positive integer; the tool loops only up to the square root of n, pairing each divisor with its complement to list all factors. A number with exactly two factors (1 and itself) is prime.
Good to know
The Factor Calculator takes a single positive whole number and lists every value that divides it evenly, then summarizes the result: how many factors there are, their total when added together, the smallest and largest, and whether the number is prime. It is handy for students checking homework on divisors and primality, for anyone simplifying fractions or finding a number's divisors quickly, and for tinkerers exploring number properties like perfect or abundant numbers.
Reach for it whenever you need the complete divisor set of one number rather than just its prime building blocks. Typical moments include verifying a divisibility test, finding all the ways to arrange or group a quantity evenly, checking whether a count is prime before using it elsewhere, or comparing the factor list of two numbers by running each in turn.
Reading the output is straightforward: the large count is the total number of factors, and the prime flag turns to "Yes" only when that count is exactly two (the number and 1). The sum adds up the whole list, which is useful for spotting special cases. For example, if the sum of all factors equals twice the number, you are looking at a perfect number, like 6 (1+2+3+6 = 12) or 28.
One practical caveat: this tool returns full factors, not a prime factorization. If you want a number expressed as a product of primes (such as 28 = 2² × 7), use the Prime Factorization Calculator instead. Also keep inputs at or below roughly 10^15, since larger values can compute slowly or lose precision due to how browsers handle big numbers.
Frequently asked questions
How does the tool decide if a number is prime?
A prime has exactly two positive factors: 1 and itself. The tool lists all factors and flags the number as prime only when the count equals 2, so 1 (one factor) is correctly treated as not prime.
Why is it fast for large numbers?
It only tests divisors up to the square root of n. Each divisor i found below the square root is paired with its complement n/i, so all factors are recovered without checking every value up to n.
Is my data uploaded anywhere?
No — this calculator runs entirely in your browser; nothing is uploaded.
Is it free?
Yes, completely free with no sign-up and no limits.
People also ask
What is the difference between factors and prime factors?
Factors are all the whole numbers that divide a value evenly, including 1 and the number itself, while prime factors are only the prime numbers whose product equals it. For 28, the factors are 1, 2, 4, 7, 14, and 28, but its prime factors are just 2 and 7.
How many factors does a number have?
It varies: prime numbers have exactly two, and the count depends on the exponents in the number's prime factorization. A number is a perfect square exactly when its factor count is odd, because one divisor pairs with itself.
Is 1 a prime number?
No. 1 has only a single factor (itself), and a prime requires exactly two distinct factors, so 1 is neither prime nor composite. The tool reflects this by reporting one factor and not flagging 1 as prime.
What is a perfect number?
A perfect number equals the sum of its proper divisors (all factors except the number itself), such as 6 and 28. You can spot one here when the listed sum of all factors is exactly double the number you entered.
Can I find the factors of a negative number?
This calculator accepts only positive whole numbers of 1 or greater. Mathematically, a negative integer has the same set of divisors as its absolute value, just with negative counterparts included.
How do I find the greatest common factor of two numbers?
You can list the factors of each number with this tool and pick the largest value that appears in both lists. For a direct answer, the Common Factor Calculator computes the greatest common factor in one step.
What does the sum of factors tell you?
The sum adds every divisor, including 1 and the number itself, and is used to classify numbers. If the sum exceeds twice the number it is abundant, if it is less it is deficient, and if it equals twice the number it is perfect.
Why does the calculator only check up to the square root?
Divisors come in pairs that multiply to the number, so once you find one factor below the square root you immediately know its partner above it. Checking only up to the square root finds every pair without testing every value, which keeps it fast.
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