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# Factoring Calculator + Online Solver With Free Steps

A **Factoring Calculator** is an online tool that is used to divide a number into all of its corresponding factors. Factors can alternatively be thought of as the number’s divisors.

Every number has a limited number of components. Enter the expression in the box provided below to use the **Factoring Calculator**.

## What Is a Factoring Calculator?

**Factoring Calculator is an online calculator used to factor the polynomials or divide the given polynomials into smaller units.**

The terms are divided in a way that when two simpler terms are multiplied together, a new **polynomial equation** is produced.

The complicated problem is typically solved using the **factoring approach** so that it can be written in simpler terms. The greatest common factor, grouping, generic trinomials, difference in two squares, and other techniques can be used to **factor the polynomials**.

The **integers** that are multiplied together to produce other integers are known as f**actors in multiplication**.

For instance, 6 x 5 = 30. In this case, the factors of 30 are 6 and 5. The factors of 30 would also include 1, 2, 3, 10, 15, and 30.

An** integer** an is essentially the ‘a’ factor of another integer ‘b’ if ‘b’ can be divided by ‘a’ with no remainder. When working with fractions and trying to identify patterns in numbers, **factors** are crucial.

The process of **prime** **factorization** consists of identifying the prime numbers that, when multiplied, give the desired result. For instance, the** prime factorization** of 120 yields the following: 2 × 2 × 2 × 3 × 5. When determining the prime factorizations of numbers, a factor tree might be useful.

It is evident from the straightforward example of 120 that **prime factorization** may get rather tiresome very fast. Unfortunately, there isn’t yet a prime factorization algorithm that is effective for really large integers.

## How To Use a Factoring Calculator

You can use the** Factoring Calculator** by following the given detailed guidelines, and the calculator will provide you with the results you need. You can follow these detailed instructions to get the value of the variable for the given equation.

### Step 1

Input the desired number into the factoring calculator’s input box.

### Step 2

Click on the **“FACTOR”** button to determine the factors of a given number and also the whole step-by-step solution for the **Factoring Calculator** will be displayed.

Finding the **factors** of a given integer is made easier using factoring calculators. Factors are those numbers that are multiplied together to create the original number. There are both positive and negative factors. There will be no remainder if the original number is divided by a factor.

## How Does Factoring Calculator Work?

A **factoring calculator** works by determining the factors of a given number. Factors are those numbers that are multiplied together to create the original number. There are both **positive** and **negative factors**. There will be no remainder if the original number is divided by a factor.

It is important to keep in mind that the factor will always be equal to or less than the given amount whenever we factor a number. Additionally, every number has at least two components, except 0 and 1. 1 and the number itself are these.

The** smallest** possible factor for a number is 1. We have three options for determining the factors of a number: division, multiplication, or grouping.

### Finding Factors

- The original number is expressed as a product of two elements using the
**multiplication approach**. The original number can be expressed as a product of two numbers in a variety of ways. As a result, every distinct set of numbers is used to create the product, which will be its factor. - When using the
**division method**, the original number is divided by all lower or equal values. A factor will be created if the remaining is zero. **Factorization by grouping**requires that we first group the terms according to their common factors. Divide the large polynomial into two smaller ones that both have terms with the same factors. After that, factor each of those smaller groups separately.

## Solved Examples

Let’s look at some of these examples to better understand the workings of the Factoring Calculator.

### Example 1

Factorize

**$3x^2$ + 6 . x . y + 9 . x . $y^2$**

### Solution

$3x^2$ has factors 1, 3, x, $x^2$, 3x and $3x^2$.

6 . x . y has factors 1, 2, 3, 6, x, 2x, 3x and 6xy and so on.

9 . x . $y^2 $ has factors 1, 3, 9, x, 3x, 9x, xy, $xy^2$ and so on.

3x is the greatest common factor we can find of all three terms.

Next, search for factors that are relevant to all terms and select the best of them. This is the most common factor. The biggest common factor in this instance is 3x.

Next, put 3x in front of a set of parenthesis.

By multiplying each term in the original statement by 3x, the terms in the parenthesis can be found.

\[ 3x^2 + 6xy + 9xy^2 = 3x(x+2y+3y^2) \]

This is known as the **distributive property**. The procedure we have been following up to now is reversed in this situation.

Now, the original expression is in factored form. Remember that factoring alters an expression’s form but not its value while evaluating the factoring.

If the answer is correct, then it must be true that \[ 3x(x+2y+3y^2) = 3x^2 + 6xy +9xy^2 \] .

You can prove this by multiplying. We must confirm that the expression has been fully factored in before moving on to the next step in the factoring process.

If we had only removed the factor “3” from $ 3x^2 + 6xy +9xy^2 $, the answer would be:

\[ 3(x^2 + 2xy + 3xy^2) \].

The answer is equal to the original expression when we multiply to check. The factor x is still present in every term, though. As a result, the expression has not been factored in entirely.

Although partially factored in, this equation is factored in.

The solution must satisfy two requirements in order to be valid for factoring:

- The f
**actored expression**must be able to be multiplied to produce the original expression. - The expression needs to be
**factored in**entirely.

### Example 2

Factorize \[ 12x^3 + 6x^2 + 18x \].

### Solution

It shouldn’t be essential to list each term’s factors at this point. You should be able to identify the main aspect in your mind. A decent approach is to consider each element separately.

In other words, get the number first, then each letter involved, rather than trying to acquire all the common factors at once.

For example, 6 is a factor of 12, 6, and 18, and x is a factor of each term. Hence \[12x^3 + 6x^2 + 18x = 6x \cdot (2x^2 + x + 3) \]

As a result of multiplying, we obtain the original and can observe that the terms included in parenthesis do not share any other characteristics, proving the correctness of the answer.

### Example 3

Factorize 3ax +6y+$a^2x$+2ay

### Solution

First, it should be noted that only part of the four terms in the expression shares a common component. For instance, factoring the first two variables together yields 3(ax + 2y).

If we take “a” from the final two terms, we obtain a(ax + 2y). The expression is now 3(ax + 2y) + a(ax + 2y) and we have a common factor of (ax + 2y) and can factor as (ax + 2y)(3 + a).

By multiplying (ax + 2y)(3 + a), we get the expression 3ax + 6y + $a^2x$ + 2ay and see that the factoring is correct.

**3ax + 6y + $a^2x$+ 2ay = (ax + 2y)(3+a) **

The first two terms are

**3ax + 6y = 3(ax+2y) **

The remaining two terms are

**$a^2x$ + 2ay = a(ax+2y) **

3(ax+2y) + a(ax+2y) is a factoring problem.

In this case, factoring by grouping was used because we “grouped” the terms by two.