Prime Factorization Calculator

Welcome to the Prime Factorization Calculator, where you can easily calculate the prime factorization of numbers.

Prime factorization is the method of expressing a number as a product of its prime factors. According to the fundamental theorem of arithmetic, any natural number greater than 1 is written as a product of prime numbers. The arrangement must be such that the product is unique.

For example, for 20, factorization results in 4 and 5. The prime factorization results in 2, 2, and 5, which are represented as 2², 5. So, the prime factorization of 20 is

20 = 4 * 5 = 2 * 2 * 5 = 2² * 5

To calculate prime factorization, the factorization must be done, but it should be represented as prime numbers only. There are two commonly used methods, one is factor tree and the other is short division.

Prime Factorization by Factor Tree Method

A factor tree is a special kind of graph that displays the factors of a number in the form of a binary tree. First, divide a number into two factors. Next, factorize the factors again until they can’t be factored. Finally, multiply all the leaf nodes of the binary tree to get the prime factorization of the number.

For example, the factor tree of 96

From left to right, all leaf nodes of this binary tree are 2, 2, 2, 2, 2, 3, so the prime factorization of 96 is

96 = 2 * 2 * 2 * 2 * 2 * 3 = 2⁵ * 3

There are various representations of factor trees, but the final prime factorization is consistent. For example, the factor tree of 96 can be represented by other factor trees.

The final result is 96 = 2 * 2 * 2 * 2 * 2 * 3 = 2⁵ * 3

Prime Factorization by Short Division Method

The short division is a basic division algorithm simplified from long division. Usually, it is used to calculate prime factorization or to find the greatest common factor. The steps are as follows: divide the number by the smallest divisible prime factor, then divide the resulting quotient by the smallest divisible prime factor. Repeat this process until the final quotient is prime.

For example, the short division of 84.

• 84 is divisible by the smallest prime factor 2. So, divide 84 by 2 and the quotient is 42.
• 42 is divisible by the smallest prime factor 2. Divide 42 by 2 and the quotient is 21.
• 21 is divisible by the smallest prime factor 3. Divide 21 by 3 and the quotient is 7.

Since 7 is a prime number, the decomposition ends here. Multiplying the divisors of each step with the final quotient to get the prime factorization of 84 is

84 = 2 * 2 * 3 * 7 = 2² * 3 * 7

The graphical representation of the short division of 84

It can be seen that all the prime numbers on the left multiplied by the bottom quotient is the final desired result.

The above are two common methods to calculate the prime factorization of a number. You can choose one of the methods according to your needs. Next, we’ll show you how to use the prime factorization calculator to get the result quickly.

The procedure to use the prime factorization calculator is as follows: