Prime Factorization Calculator
What is a prime number?
A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number.
Examples of prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97...
Examples of composite numbers: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30...
The fundamental theorem of arithmetic states that every natural number greater than 1 can be written as a product of prime numbers in a unique way (up to the order of the factors). For example, 60 = 5 × 3 × 2 × 2.
What is prime factorization?
Prime factorization is the decomposition of a composite number into a product of prime numbers. There are several methods to find the prime factorization of a number.
Trial division
One method for finding the prime factorization of a composite number is trial division. Test integers by dividing the composite number by each integer until the result is no longer an integer.
Example: Prime factorization of 820
Prime decomposition (Factor tree)
Another method is to create a factor tree. Start by writing the number at the top, then break it down into factors. Continue breaking down composite factors until all factors are prime.
Example: Prime factorization of 820
Two different factor trees for 820: