Prime Factorization Calculator
Enter a whole number from 2 to 1,000,000,000,000 to see it written as a product of primes.
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Formula
Trial division: divide by 2, then by odd numbers 3, 5, 7, ... while the divisor squared is at most what remains; anything left above 1 is prime. The number of divisors is (e1 + 1) × (e2 + 1) × ... for exponents e1, e2, ....
Worked example
360 ÷ 2 = 180, ÷ 2 = 90, ÷ 2 = 45, then 45 ÷ 3 = 15, ÷ 3 = 5, and 5 is prime. So 360 = 2^3 x 3^2 x 5, with 3 distinct primes and (3+1)(2+1)(1+1) = 24 divisors.
Frequently asked questions
What is prime factorization?
It is writing a whole number as a product of prime numbers. Every number above 1 has exactly one such product. For example, 360 = 2^3 x 3^2 x 5, which means 2 × 2 × 2 × 3 × 3 × 5.
How does trial division find the factors?
Divide by 2, then by each odd number 3, 5, 7 and so on, as long as it divides evenly, and stop when the divisor squared exceeds what is left. Whatever remains above 1 is itself prime. For 360 the steps are 360 ÷ 2 ÷ 2 ÷ 2 = 45, then 45 ÷ 3 ÷ 3 = 5.
How many divisors does a number have?
Add 1 to each exponent and multiply the results. For 360 = 2^3 x 3^2 x 5 that is (3+1) × (2+1) × (1+1) = 24 divisors.
What if the number is prime?
A prime is its own only prime factor, so the answer is the number itself and it has exactly 2 divisors. 97 is an example. The number 1 has no prime factors, so it is not accepted.