Prime Factorization Calculator
Check whether a number is prime and break it down into its prime factors.
About this tool
Finds the prime factors of any whole number from 2 up to 9,007,199,254,740,991 (the largest whole number a browser can store exactly) by trial division, and shows them in exponent form.
Every whole number above 1 is either prime or can be written as a product of primes in exactly one way. This calculator finds that product for you, tells you whether your number is prime, and counts how many divisors it has. Use it for homework on factor trees, for simplifying fractions and square roots, or to check whether a large number is prime.
How to use the Prime Factorization Calculator
- Type a whole number of 2 or more.
- Read the prime factorization in exponent form, for example 2^3 × 3^2 × 5.
- See whether the number is prime and how many divisors it has.
Factorizing 360
360 ÷ 2 = 180, ÷ 2 = 90, ÷ 2 = 45; 45 ÷ 3 = 15, ÷ 3 = 5; and 5 is prime. So 360 = 2 × 2 × 2 × 3 × 3 × 5 = 2^3 × 3^2 × 5. Adding one to each exponent and multiplying gives the number of divisors: (3 + 1) × (2 + 1) × (1 + 1) = 24. By contrast, 97 has no factors other than 1 and itself, so it is prime.
How the factors are found
The calculator divides by 2 as many times as it can, then by 3, 5, 7 and every odd number after that, until the divisor squared is bigger than what is left. Whatever remains above 1 is itself prime. You only need to test up to the square root because if a number had two factors both bigger than its square root, their product would be too large. That makes even 15-digit numbers quick: 600,851,475,143 breaks down to 71 × 839 × 1,471 × 6,857 in a fraction of a second. The fundamental theorem of arithmetic says this factorization is unique, apart from the order of the factors. The number 1 is neither prime nor composite.
Frequently asked questions
Is 1 a prime number?
No. A prime has exactly two different divisors, 1 and itself. The number 1 has only one divisor, so it is neither prime nor composite.
Is 2 the only even prime?
Yes. Every other even number can be divided by 2, so it has at least three divisors.
What is a factor tree?
A diagram that splits a number into two factors, then splits each factor again until only primes are left. The primes at the ends of the branches are the prime factorization.
How do I find the number of divisors?
Write the number in exponent form, add 1 to each exponent and multiply. 72 = 2^3 × 3^2 has (3 + 1) × (2 + 1) = 12 divisors.