Factor Calculator

This factor calculator lists every factor of a whole number, shows the factor pairs and gives the prime factorization. It also tells you if the number is prime. Type a number up to 999,999,999,999 and the answer shows as you type.

Enter a whole number from 1 to 999,999,999,999.

9 factorsFactors of 36

All factors

1, 2, 3, 4, 6, 9, 12, 18, 36

Factor pairs

    Prime factorization

    22 × 32

    Quick facts

    Number of factors: 9. Sum of factors: 91. Type: Composite.

    How to use the factor calculator

    1. Type a whole number into the box.
    2. Read the list of all factors, from smallest to largest.
    3. Check the factor pairs. Each pair multiplies to give your number.
    4. Read the prime factorization and see if the number is prime or composite.

    What is a factor?

    A factor of a number divides it with nothing left over. Since 12 ÷ 3 = 4, the number 3 is a factor of 12. Every whole number has 1 and itself as factors.

    Factors of common numbers

    The factors of 12 are 1, 2, 3, 4, 6 and 12. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36. The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50 and 100. Type any of these into the calculator to check.

    Factor pairs and prime factorization

    A factor pair is two factors that multiply to give your number, such as 4 × 9 = 36. Prime factorization writes a number as a product of primes. For 36 it is 2 × 2 × 3 × 3, which is written 2² × 3². You can count the factors from this: add 1 to each power and multiply. For 36 that is (2 + 1) × (2 + 1) = 9 factors.

    How the calculator finds the factors

    It divides your number by primes, starting with 2, to build the prime factorization. It then combines those primes in every possible way to list all the factors and sorts them from small to large.

    Divisibility rules that save time

    • A number is divisible by 2 if its last digit is even.
    • A number is divisible by 3 if the sum of its digits is divisible by 3.
    • A number is divisible by 5 if it ends in 0 or 5.
    • A number is divisible by 9 if the sum of its digits is divisible by 9.
    • A number is divisible by 10 if it ends in 0.

    Greatest common factor

    The greatest common factor of two numbers is the largest factor they share. The factors of 12 are 1, 2, 3, 4, 6 and 12. The factors of 18 are 1, 2, 3, 6, 9 and 18. The shared factors are 1, 2, 3 and 6, so the greatest common factor is 6. Run each number through the factor calculator and compare the two lists.

    Why factors matter

    Factors help you simplify fractions, share items into equal groups and find common denominators. They also help you test a number by hand before you use the factor calculator. For example, 4,572 ends in an even digit, so 2 is a factor. Its digits add up to 18, which is divisible by 3 and by 9, so 3 and 9 are factors too.

    Once you know the prime factorization, you can build every factor from it. This is the same method the calculator uses, so you can check its answer by hand.

    Frequently asked questions

    Is 1 a prime number?

    No. A prime number has exactly two factors, and 1 has only one. The number 1 is also not composite.

    What are the factors of a prime number?

    A prime number has only two factors: 1 and itself. The factors of 13 are 1 and 13.

    What is the difference between a factor and a multiple?

    A factor divides a number with nothing left over. A multiple is what you get when you multiply the number by a whole number. 3 is a factor of 12, and 12 is a multiple of 3.

    Can I use zero, negative numbers or decimals?

    No. The factor calculator works with whole numbers from 1 up to 999,999,999,999.

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