Factorial decomposition

If you need to know the decomposition into factors of a numberyou are in the right place. Here you will find a calculator that will allow you to know instantly the factorization of any positive integer.

In case you enter a number that cannot be broken down into factors, it will also show you that the number you have entered is a prime number.

What is the factorization of a number?

How to factor a number

When we talk about factorizing a number, what we are doing is decomposing it as a product of prime factors which, when multiplied together, give us the starting number.

For example:

  • The number 6 can be decomposed as a product of 2 x 3
  • The number 27 can be decomposed as a product of 3 x 3 x 3

To factor a number, you must perform divisions by its prime divisors until we get a one in the quotient. To do this, the vertical bar method is usually used, such that:

  • on the left side of the bar, we write the quotients of the division
  • to the right of the bar, we write the prime divisors we get

One of the clear applications of the decomposition into prime factors consists of co calculate the least common multipleThis is very important for doing other operations such as addition or subtraction of fractions.

Factoring polynomials

Factoring polynomials also consists of decomposing into factors starting from a common factor and then taking out the roots. Let's look at some cases in particular.

Difference of squares

They are polynomials of the type:

a2 - b2 = (a + b) - (a - b)

In these cases we can decompose into factors and extract the roots relatively easily. For example, if we have:

x2 - 25 = (x2 + 5) - (x2 - 5)

The roots of the above polynomial are x=5 and x=-5.

Polynomials of second degree

In this case, the appearance of the polynomial is of this type:

ax2 + bx + c = 0, where a is non-zero

There are also variations that can make simplifying this type of polynomial to be done in one way or another, so we recommend you to visit the following web site where we explain how to do it solving quadratic equations.

In the link we have just left you will learn to factoring second degree polynomials.

How to factor online

Factorization of a number

Our online factoring calculator has a very simple operation. Just type the number you want to decompose into prime factors and press the calculate button to obtain its factorization.

13 thoughts on “Descomposición factorial”

  1. Hello, I congratulate you for your very good page, but I want to tell you that there is a small error and it would be great if you could correct it so as not to misinform others, in the exercise x^4-25 it says that the roots are 5 and -5, but in reality it is (square root of 5) and minus square root of 5) that, thanks....

    • Indeed Victor, you are right and there was a typo in that statement. We have already corrected it, so thank you very much for the warning.

      Best regards!

  2. thank you very much I will donate you at the end to the world's best caculadora thank you very much enseri above with a polite and atbtote ayudznte every hour opara to see the comments dela people thank you truly 5 stars

    • Hi Javier,

      I can't tell you the result of the factorization because the number is too big and there is an overflow, so the result is incorrect: 5 x 811 x 185483 x 6229507 x 2267

      I have tried to solve it with Excel and it is exactly the same.

    • Hello Saul,

      To factorially decompose the equation you propose, you can do the following:

      am-bm+an-bn = a(m+n) - b(m+n) = (m+n)(a-b)


    • Hello Alberto José,

      Yes, a negative number can also be factored although in this case we will have several possible factoring combinations.

      For example, for the negative number -10 we will have that its factorization can be:

      2 x -5
      -2 x 5

      As you can see, both combinations result in the number -10.


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