Find every factor of a whole number in an instant. Enter a positive integer and the calculator lists all of its factors (divisors), the factor pairs, how many factors there are, and the prime factorization. Switch to the second tab to find the common factors shared by two numbers.
The factor calculator finds every factor of a whole number and lays them out clearly for you. Type in any positive integer and it returns the complete list of factors (also called divisors), arranges them into neat factor pairs, counts how many there are, and shows the number's prime factorization. It also has a second mode that finds the common factors shared by two numbers — handy for simplifying fractions and finding the greatest common factor. Whether you are working through math homework, teaching factoring, or just curious about the building blocks of a number, this tool does the searching for you in an instant.
Factoring by hand means testing divisor after divisor, which is slow and error-prone for larger numbers. This calculator checks every possibility efficiently and never misses one, so you get the full, correct list every time.
A factor of a whole number is any whole number that divides into it evenly, leaving no remainder. For example, 3 is a factor of 12 because 12 ÷ 3 = 4 with nothing left over, while 5 is not a factor of 12 because 12 ÷ 5 leaves a remainder of 2. Factors are also called divisors, and the two words mean exactly the same thing in this context. Every whole number has at least two factors — 1 and the number itself — because 1 divides everything and every number divides itself. Numbers with exactly those two factors and no others are called prime numbers; numbers with more than two factors are composite.
Factors always come in pairs. If a number d is a factor of n, then n ÷ d is also a factor, and together they multiply back to n. That is why factors are so naturally displayed as pairs, and it is the key idea that makes finding them efficient.
To find all the factors of a number n, the calculator tests each whole number from 1 up to the square root of n. Every time it finds a divisor d that divides n evenly, it records both d and its partner n ÷ d, since factors come in pairs. Checking only up to the square root is enough to catch every pair, because in any factor pair one member is always less than or equal to the square root and the other is greater than or equal to it. This makes the search fast even for large numbers. The calculator then sorts the complete list in ascending order and removes any duplicate (which happens once, for perfect squares, where the square root pairs with itself).
For the prime factorization, the calculator repeatedly divides the number by the smallest prime that fits — first by 2 as many times as possible, then 3, then 5, and so on — until only 1 remains, collecting the primes as it goes.
Take the number 60. Testing divisors from 1 upward, the calculator finds these factor pairs: 1 × 60, 2 × 30, 3 × 20, 4 × 15, 5 × 12, and 6 × 10. Listing every number that appears gives the full set of factors:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
That is 12 factors in total. The prime factorization of 60 is 2 × 2 × 3 × 5, usually written 2² × 3 × 5. This is the default example loaded into the calculator, so you can press Calculate to see the full breakdown and then enter your own number.
These three terms are often confused, so it helps to separate them clearly:
A simple way to keep them straight: factors are smaller than or equal to your number, while multiples are larger than or equal to it.
A factor pair is a set of two numbers that multiply together to give your original number. Because factors always come in twos, listing the pairs is a tidy way to see them all and a great check that none have been missed. For 24, the factor pairs are 1 × 24, 2 × 12, 3 × 8, and 4 × 6 — giving the eight factors 1, 2, 3, 4, 6, 8, 12, and 24. Factor pairs are especially useful in geometry and everyday problems: the pairs of a number are exactly the possible whole-number dimensions of a rectangle with that area, so the factor pairs of 24 tell you a 24-tile floor can be laid out as 1×24, 2×12, 3×8, or 4×6.
The second tab compares two numbers and finds their common factors — the numbers that divide evenly into both. For 24 and 36, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 and the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The numbers appearing in both lists are 1, 2, 3, 4, 6, and 12, so those are the common factors, and the largest of them, 12, is the greatest common factor (GCF). Finding common factors is the essential step in reducing a fraction to its simplest form: dividing both the numerator and denominator of 24/36 by their GCF of 12 gives 2/3. It is also used to split things into equal groups and to compare ratios.
The prime factorization of a number expresses it as a product of prime numbers only. Every whole number greater than 1 has exactly one prime factorization (ignoring the order of the factors) — a result so important it is called the Fundamental Theorem of Arithmetic. For example, 60 = 2² × 3 × 5 and 100 = 2² × 5². Prime factorization is the backbone of many other calculations: it lets you find the greatest common factor and least common multiple quickly, simplify fractions and radicals, and understand the deep structure of a number. This calculator shows the prime factorization alongside the full factor list so you can see both the building blocks and every number they can combine to form.
You do not always have to list every factor to know how many there are. Once you have the prime factorization, there is a neat shortcut: add one to each exponent and multiply the results. For 60 = 2² × 3¹ × 5¹, that is (2 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 = 12 factors, which matches the list exactly. This is why highly composite numbers — those with many small prime factors, like 12, 24, 36, and 60 — have so many divisors, and it explains why such numbers show up so often in measurements, time (60 seconds, 60 minutes, 24 hours), and packaging. The calculator reports the factor count for you, but the shortcut is a satisfying way to check it.
When factoring by hand, a handful of divisibility rules let you spot small factors at a glance without doing the division:
These rules are a great way to start a factor list quickly, and they build number sense. The calculator, of course, checks every possibility for you, but knowing the rules helps you sanity-check the results and factor small numbers in your head.
Here are the factor lists for a few frequently searched numbers, which you can confirm in the calculator:
Factors even give rise to some intriguing categories of numbers, based on the sum of a number's proper factors (all its factors except the number itself). If that sum equals the number, it is a perfect number — 6 is the smallest, since its proper factors 1, 2, and 3 add up to 6. If the sum is greater than the number, it is abundant (like 12, whose proper factors 1, 2, 3, 4, and 6 total 16), and if the sum is smaller, the number is deficient (like any prime, whose only proper factor is 1). These ideas have fascinated mathematicians since antiquity, and they all start from the simple act of listing a number's factors — exactly what this calculator does. The "sum of factors" figure in the results makes it easy to explore these classifications yourself.
A factor is a whole number that divides evenly into another number with no remainder. For instance, 4 is a factor of 20 because 20 ÷ 4 = 5 exactly. Factors are also called divisors.
Test each whole number from 1 up to the square root of your number; whenever one divides evenly, both it and the quotient are factors. This calculator does that automatically and lists every factor in order.
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60 — twelve factors in all. Its prime factorization is 2² × 3 × 5.
Factors are all the whole numbers that divide evenly into your number; prime factors are only those factors that are prime. The prime factors of 12 are 2 and 3, while all its factors are 1, 2, 3, 4, 6, and 12.
Yes, but this calculator focuses on positive integers and their positive factors. Every positive factor has a matching negative one, so if you need the negatives, just put a minus sign in front of each listed factor.
List the factors of each number and pick out the ones that appear in both lists. The largest shared factor is the greatest common factor. The "Common Factors" tab does this for you and highlights the GCF.
This Factor Calculator is provided for educational and general informational purposes. It works with positive whole numbers and lists their positive factors. Results are computed exactly for integers within the supported range.