Use this free factor calculator to find all the factors of a whole number, its factor pairs and its prime factorization, drawn as a factor tree. You also see the number of factors, their sum, and whether the number is prime or composite, with the steps shown. Two more tabs give a quick GCF and LCM of up to 10 numbers, and check whether one number is a factor or multiple of another. For the full working of the GCF and the LCM, use the GCF Calculator and the LCM Calculator. Tables of factors of common numbers and of 1 to 100, divisibility rules and the prime numbers up to 100 are underneath. It is free and instant, and your numbers stay in your browser.
What are factors?
The factors of a number are the whole numbers that divide into it exactly, with nothing left over. To find them, try dividing by 1, 2, 3 and so on. Each time it divides evenly you have found a pair. You only need to try numbers up to the square root of the number, because the rest come from the pairs.
1, 2, 3, 4, 6, 8, 12, 24They come in pairs: 1 × 24, 2 × 12, 3 × 8 and 4 × 6. The square root of 24 is about 4.9, so trying 1, 2, 3 and 4 is enough. The calculator also shows the number of factors (8) and their sum (60).
Another example: the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36. They come in the pairs 1 × 36, 2 × 18, 3 × 12, 4 × 9 and 6 × 6. Perfect squares such as 36 have an odd number of factors (9), because the square root pairs with itself.
Prime numbers and prime factorization
A prime number has exactly two factors: 1 and itself. 97 is prime, but 33 is not, because its factors are 1, 3, 11 and 33. The number 1 is not prime. Every other whole number can be written as a product of primes, called its prime factorization. For example, 24 = 2³ × 3, which means 2 × 2 × 2 × 3, and 360 = 2³ × 3² × 5. A factor tree shows the same thing: split the number into two factors, then split each one again, until only primes are left.
How many factors does a number have?
Write the number as a product of primes, add 1 to each power, and multiply. For 24 = 2³ × 3 that is (3 + 1) × (1 + 1) = 8 factors. For 360 = 2³ × 3² × 5 it is (3 + 1) × (2 + 1) × (1 + 1) = 24 factors.
Greatest common factor (GCF)
The GCF (also called the greatest common divisor, GCD, or highest common factor, HCF) of two or more numbers is the biggest number that divides all of them. The GCF of 12 and 18 is 6, and so is the GCF of 12, 18 and 24. One way to find it is to write each number as a product of primes and multiply the primes they all share, using the lowest power. Another is the Euclidean algorithm: divide the bigger number by the smaller, then the smaller by the remainder, and repeat until the remainder is 0. You use the GCF to simplify fractions: divide the top and bottom of 12/18 by 6 to get 2/3. To do the simplifying for you, use the Fraction Calculator. For the working shown three ways, use the GCF Calculator.
Least common multiple (LCM)
The LCM is the smallest number that all the numbers divide into. The LCM of 12 and 18 is 36, and the LCM of 12, 18 and 24 is 72. It is the number you use as a common denominator when adding fractions. For two numbers, LCM = (first × second) ÷ GCF: 12 × 18 ÷ 6 = 36. The LCM Calculator shows four ways to find it and lists the common multiples.
Factors and multiples
A factor divides a number with no remainder, and a multiple is what you get by multiplying a number by 1, 2, 3 and so on. 6 is a factor of 24, and 24 is a multiple of 6. To check whether one number is a factor of another, divide: 24 ÷ 6 = 4 with no remainder, so yes. 24 ÷ 5 = 4 remainder 4, so 5 is not a factor of 24. The “Is it a factor?” tab does this for any two numbers.
Quick divisibility tests
These shortcuts tell you if a number has a certain factor without dividing. A number is divisible by 2 if it ends in 0, 2, 4, 6 or 8; by 3 if its digits add up to a multiple of 3 (24: 2 + 4 = 6); by 5 if it ends in 0 or 5; by 9 if its digits add up to a multiple of 9; and by 10 if it ends in 0. Divisible by both 2 and 3 means divisible by 6. The table on this page checks your number against all of them.
What you can enter
For factors, enter any whole number from 1 up to 1,000,000,000,000. For the GCF and LCM, enter between 2 and 10 whole numbers, separated by commas or spaces. Factors are shown as positive numbers, as usual. Every factor also has a negative partner, such as −2 and −3 for 6.
