Contents

**Factors of -6: Prime Factorization, Methods, Tree, and Examples**

TheÂ **factors of -6**Â are all those numbers by which -6 can beÂ **divided equally**.Â The numbers that can split an original number evenly are called factors.

Additionally, when two integers are multiplied together to yield the number -6 as a result, they are referred to as the pair factors of the -6.

As an illustration, the factor pairs for -6 are represented by the symbols (1,-6) and (-1,6). The original number should be produced when we multiply a pair of elements. For example, if we multiply -1 by 6, we get -6. As a result, we can take into account both**Â positive and negative**Â factor pairs of 6.

We shall employ theÂ **factorization method**Â to discover the factors of the number -6. In the factorization method, the numbers 1 and -6 are taken as factors of -6 first. Then, the other pair of multiples of -6 are found, and the result is returned as an original number.

Read the article below to find**Â factors of -6 in pairs**Â as well as the division method to find the prime factors of -6 to better comprehend this strategy.

**What Are the Factors of -6?**

**The factors of -6 are 1, -1 2, -2, 3, -3, 6, and -6 as they evenly divide -6 without any remainder.**

The**Â factors of -6Â **are the numbers that divide -6 perfectly without leaving a residual. In other words, the pairs of numbers that when multiplied together provide the original number -6 are the factors of -6.

**How To Calculate the Factors of -6?**

You can calculate theÂ **factors of -6**Â byÂ discovering and compiling a list of all the factors of -6 and examining every number up to and including -6. The numbers that are completely divided by -6 leaving no remainder are considered to be its factors.

The factors of -6 can be found as:

**-6 $\div$ 1= -6**

**-6 $\div$ 2= -3**

**-6 $\div$ 3= -2**

**6 $\div$ -1= -6**

**6 $\div$ -2= -3**

**6 $\div$ -3= -2**

So, the factor list of -6 is given as:

**Factor List: 1, -1, 2, -2, 3, -3, 6, and -6.**

-6 is a negative integer therefore it can have both positive as well as negative factors with the condition that their multiplication in pairs will always result in a negative 6. Let us explore some interesting facts about number -6.

**Important Properties**

Following are some important facts about -6 that help in determining its factors.

- -6 is aÂ
**negative integer.** - 6 is a
**composite number**Â therefore it has more than 2 factors. - It is an
**Â even number**Â so 2 is the factor of -6. - -6 is also theÂ
**multiple of 3**Â therefore 3 is also its factor. - TheÂ
**factors of -6**Â are not in the form of decimals or fractions. - TheÂ
**total number**Â of factors of -6 is 8 including the negative as well as the positive factors.

**Factors of -6 by Prime Factorization**

The**Â prime factorization**Â of -6 is given asÂ (**-2 x 3 = -6)**

Finding the prime numbers that are multiplied together to produce the original number is the process ofÂ **prime factorization**.

Note that while every occurrence of a particular prime factor is included in the prime factorization of -6, the number 1 is excluded.

Identifying or finding the group of prime numbers that, when multiplied together, result in the original number -6 is known as theÂ **prime factorization or integer factorization of -6.**Â This is also referred to as -6 prime decomposition.

**Prime Factorization of -6**Â is the process of locating the prime factors of -6. Divide -6 by the smallest prime number you can find to obtain the prime factors of -6. The next step is to divide the outcome by the smallest prime integer. Continue doing this until you have 1.

TheÂ **prime factorization**Â -6 is shown below in figure 1:

**Factor Tree of -6**

The**Â factor tree of -6**Â is shown below in figure 2:

The factor tree is the pictorial description of prime factors decomposition of -6.

**Factors of -6 in Pairs**

**Factor pairs**Â of -6 are those numbers that when multiplied together give -6 as the result.

We must first obtain all of the factors of -6 to calculate the factor pairs of -6. Once you have a list of every one of those factors, you can pair them together to create a list of every pair of factors.

The factor pairs of -6 are determined as follows:

**1 x âˆ’6 = âˆ’6Â **

**2 x âˆ’3 = âˆ’6Â **

**6 x âˆ’1 = âˆ’6Â **

**âˆ’1 x 6 = âˆ’6Â **

**âˆ’2 x 3 = âˆ’6Â **

So, the factor pairs of -6 are given as:

**(1,âˆ’6)**

**(âˆ’1,6)**

**(âˆ’2,3)**

**(âˆ’3,2)**

## Factors of -6 Solved Examples

Here are some solved examples incorporating factors of -6.

### Example 1

What are the common factors between -6 and 8?

#### Solution

First, list factors of-6 and 8.

The factors of -6 are listed as -6, -3, -2, -1, 1, 2, 3, and 6

and the positive and negative factors of 8 are -8, -4, -2, -1, 1, 2, 4, and 8

Now identify the factors shared by both -6 and 8; these will be common factors between -6 and 8.

**Therefore, -1, -2, 1, and 2 are the common factors between -6 and 8.**

### Example 2

Jimmyâ€™s factor for the number -6 is (-2). How will he obtain the second factor?

#### Solution

The factor equation can be written as:

**âˆ’6 = âˆ’2 x factorÂ **

So, the second factor will be given as:

**Â âˆ’6 âˆ’2 = factor**

**Factor = 3Â **

**The second factor is therefore 3.**

### Example 3

Find the greatest common factor between -6 and 12?

#### Solution

First, list factors of-6 and 12.

The factors of -6 are listed as -6, -3, -2, -1, 1, 2, 3, and 6

and the factors of 12 are 1, 2, 3, 4, 6 and 12Â

the common factors between -6 and 12 are 1, 2, and 3 and from these, the greater common factor is 3Â

**so therefore the greatest common factor between -6 and 12 is 3Â **

### Example 4

What are the common factors between -6 and 20?

#### Solution

First, list factors of 6 and 20.

The factors of -6 are listed as -6, -3, -2, -1, 1, 2, 3, and 6

and the positive and negative factors of 20 are -20, -10, -5, -4, -2, -1, 1, 2, 4, 5, 10 and 20.

Now identify the factors shared by both -6 and 20; these will be common factors between -6 and 20.

**Therefore, -1, -2, 1, and 2 are the common factors between -6 and 20.**

*Images/mathematical drawings are created with GeoGebra.*