Prime Factorization Calculator

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What is the meaning of prime factor & what is meant by prime factorization?

As far as the number is concerned then the prime factors can be defined in the following manner. Essentially, prime factors of a said positive integer is stated to be the prime numbers which help an integer divide in an equal  manner. On the hand, the prime factorization of a positive integer is nothing but a list of a prime factor’s integer along with their multiplicities.

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What is integer factorization?

And as for the integer factorization, then it is known as the process to determine the factors. In addition to this, the fundamental theorem of the arithmetic clearly states that every positive integer shall certainly have at the least 1 prime factorization. To explain this prime factorization further, look at the example mentioned below to understand this prime factorization formula.

\(360\,=\,2\, \times \, 2 \, \times \, 2 \, \times \, 3 \, \times \, 3 \, \times \,5\, =\, 2^3 \, \times \, 3^2 \, \times \, 5\)

As per the above equation, the factors which are 2 / 3 / 5 have the multiplicities in the following order 3, 2 & 1 respectively.

How to find the prime factorization?

In essence, prime factorization is nothing but the breaking down of the numbers to the simplest form.

Formula to find prime factorization

One can learn prime factorization with the help of the example which has been mentioned below –

\(48\,=\,8\, \times \, 6 \)

From the above equation, 8 can be written in the following manner –

\(8\,=\,4\, \times \, 2 \)

On the other hand, number 4 can be simplified as it has been explained below –

\(\Rightarrow 4\,=\,2\, \times \, 2 \)

Whereas, the number 6 can further be simplified with the help of numbers 3 & 2 like the way it has been mentioned here –

\(6\,=\,3\, \times \, 2 \)

\(E.g. \, 24\,=\,2^3\, \times \, 3 \)

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What is meant by perfect squares?

Basically, perfect square numbers can without any trouble be identified by the fact that the prime factors have even multiplicities. The best example for such a perfect square can be 144 is which further known as the square of 12.  The prime factors of 144 are as follows –

\(144\,=\,2 \, \times \, 2\, \times \,2 \, \times \,2\, \times \,3 \, \times \,3=2^4 \times 3^2 \)

However, one can arrange the same numbers in a different order to come up with an equation like the following stated –

\( 144\,=\,2\, \times \,2 \, \times \,2 \, \times \,2 \, \times \,3 \, \times \,3 \, =\, (2 \, \times \,2 \, \times \,3) \, \times \,(2 \, \times \,2 \, \times 3)=(2\times2\times 3)^2= (12)^2\)

What is the use of a prime factorization calculator?

This online prime factorization calculator will be able to find the prime factors of an integer apart from having them presented in the form of a set of the prime factors or as a set of the prime factor raised to power of its frequency or even showing as the work for current factorization with the help of a prime factor tree (in some cases).

How to use a prime factorization calculator?

To make use of the online prime factorization calculator, you will have to first enter the number which is to be factored & click on calculate to know the answer.