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## What is meant by factorization?

Factorization has other synonyms such as factoring & in mathematics it is stated to be the decomposition of the object in to the product of some other objects or the factors. These objects can be either a number or a matrix or even a polynomial as well. In addition to this, these factors or the objects when multiplied will come up as the original answer or the original object. The best example for such a factoring or the factorization can be the seen in the following examples –

## Prime Factorization Calculator

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\(e.g.\, 15\, =\, 3\, \times \, 5\)

\(or\, x^{2}\, -\, 4\, =\, (\, x\, -\, 2\, )\, (\,x \,+ \, 2\, )\)

## What is use of factoring?

The main use of factoring is to reduce numbers to the basic building blocks. Therefore, with the help of this factorization, one can reduce the numbers to prime numbers or for that matter the polynomials to the irreducible polynomials. Besides this, the factoring integers are covered by fundamental theorem of arithmetic on one hand while the factoring polynomials are covered by the fundamental theorem of algebra.

And as far as the co – efficient of the polynomial to the root is in question then the Viete’s formula comes in to the picture. However, another term well – known as the expansion happens to be the opposite of the polynomial factorization. But the integer factorization for the large integers is quite a problem. While on the other hand, one can see that a matrix will be factorized as well & this shall happen in the form of special types. One of the best example for such a thing would be the use of an octagonal or the triangular or the unitary matrix.

In addition to this, there are various other things such as the QR decomposition or the LQ or QL or RQ & RZ. There is another example for the factorization of the function & it is the composition of the other functions which have properties like the following (1) every function will be able to be viewed as composition of surjective function that too with the injective function. Moreover, such a situation is generalized by the factorization systems.

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### How to find the number of factors in a number?

In order to find the number of factors in a given number, let us take an example which has also been given in detail below. Let us now assume that the number is 72.

\(72\, =\, 2 \, \times \, 36\)

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

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

\(= 2^{3}\, \times \, 3^{2}\)

From the above equation, the exponents which are 3 & 2 respectively are taken & 1 is added to them. Therefore, they turn in to 4 as well as 3. Due to the addition of 1 to the exponents, we have the following factors for 72. One has to also remember that the exponents are to be multiplied so that we get the factors for 72.

Therefore,\(4 \, \times \, 3\, =\, 12\)

And the factors for 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 & 72 respectively.

## How to use a factor calculator?

If you wish to use a factor calculator then you will have to first enter the factor in the field marked & then click on the tab calculate to get the factor or factors of the said number.

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