Factors and Prime Factorisation Calculator
Enter a whole number of up to 20 digits to get all its factors and factor pairs, its prime factorisation in index form with the working, the count and sum of factors, and what kind of number it is.
Commas and spaces are ignored.
Worked examples
A composite number
360
2³ × 3² × 5, 24 factors
Factors add up to 1,170.
A perfect number
28
Factors 1, 2, 4, 7, 14, 28
1 + 2 + 4 + 7 + 14 = 28.
About Factors and Prime Factorisation Calculator
A factor of a number is a whole number that divides it exactly. The factors of 12 are 1, 2, 3, 4, 6 and 12, and they come in pairs that multiply to the number: 1 × 12, 2 × 6 and 3 × 4. Every whole number above 1 is either prime, with just two factors, or can be written in exactly one way as a product of primes. For example, 360 is 2 × 2 × 2 × 3 × 3 × 5, written in index form as 2³ × 3² × 5.
The page divides by the smallest prime that fits, again and again, and shows each step as you would in a factor tree. For large numbers it uses faster methods than trial division, so even a 20-digit number is done in a moment. From the prime powers it counts the factors (360 has 4 × 3 × 2 = 24) and adds them up. If the factors other than the number itself add up to the number, it is perfect, like 6 and 28. If they add to more it is abundant, and if less it is deficient. Prime factors help with simplifying fractions and roots and with finding the highest common factor.
How to use Factors and Prime Factorisation Calculator
- Type a whole number of up to 20 digits. Commas and spaces are ignored.
- Read the number of factors and what kind of number it is.
- See the prime factorisation in index form and the full list of factors and pairs.
- Follow the division steps to see how the primes were found.
Common uses
- Simplifying fractions and surds
- Finding common factors and multiples
- Sharing items into equal groups or rows
- Number theory homework on prime and perfect numbers
Frequently asked questions
What is a prime number?
A whole number above 1 whose only factors are 1 and itself, such as 2, 3, 5, 7, 11 and 13.
How do I know a number is a perfect square?
It has an odd number of factors, because one factor pairs with itself. In its prime factorisation, every prime has an even power.
What is a perfect number?
A number equal to the sum of its factors other than itself. 6 is perfect because 1 + 2 + 3 = 6, and so is 28.
How are huge numbers factorised?
The page removes small primes first and then uses faster methods for the rest. Numbers of up to 20 digits are handled. For a number with two very large prime factors it may report that it could not finish.
What is the difference between factors and multiples?
Factors divide into a number. Multiples are what you get by multiplying a number. 3 is a factor of 12, and 12 is a multiple of 3.