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Factors of 12: Prime Factorization, Methods, and Examples

Factors of 12 are the numbers that divide evenly with 12 when all other numbers are divided by 12 up to that number itself.

Factors of twelve

Figure 1 – All possible factors of 12

When we refer to the factors of 12, we mean all the positive and negative integers that may be divided by 12 equally. The result would be another factor of 12 if you took 12 and divided it by one of its factors.

Since 12 is a composite number, we can conclude that composite numbers are those that have more than two elements. Composites are another name for these numbers.

In contrast to prime numbers, which only have the number itself and the number 1 as their factors, composite numbers have more elements. Since they can be divided by more than two integers, any natural numbers that are not prime numbers are composite numbers.

This short guide will demonstrate that our solution is correct, we will offer you the definition of Factors of 12, demonstrate how to find Factors of 12, give you all Factors of 12, explain how many Factors 12 has, and give you all Factor Pairs of 12. Let’s start now!

What Are the Factors of 12?

The factors of 12 are 1, 2, 3, 4, 6, and 12, since all of these divide 12 evenly, leaving no residual.

The numbers that divide 12 perfectly without producing a remainder are known as its factors. Being an even composite number, 12, in addition to 1 and 12, has a lot of other factors. The number 12 also has both positive and negative factors.

How To Calculate the Factors of 12?

You can calculate the factors of 12 by discovering and compiling a list of all the factors of 12 then examining every number up to and including 12 and determining which numbers produce an even quotient.

This approach is really basic and easy. There are only five parts to the complete procedure.

First, think about the number 12. Divide it evenly amongst all the numbers from 1 to 12. Record the outcomes. The division produces the following factors:

\[ \dfrac{12} {1} =  12\]

\[ \dfrac{12} {2} =  6\]

\[ \dfrac{12} {3} =  4\]

\[ \dfrac{12} {4} = 3\]

\[ \dfrac{12} {5} = 2.4 \]

\[ \dfrac{12} {6} = 2\]

\[ \dfrac{12} {7} = 1.7\]

\[ \dfrac{12} {8} = 1.5\]

\[ \dfrac{12} {9} = 1.3\]

\[ \dfrac{12} {10} = 1.2\]

\[ \dfrac{12} {11} = 1.09\]

\[ \dfrac{12} {12} = 1 \]

Reject the decimals and filter out the positive integer quotient for the aforementioned.

Here are the factors of 12: 1, 2, 3, 4, 6, and 12.

Negative integers are also included in the factors of 12. The aforementioned procedure must be repeated while taking into account negative numbers to determine how many components in 12 include negative integers.

Therefore, all the integers we divided (used as divisors earlier) to arrive at an even number are the positive factors of 12. Here is a list of every positive factor of 12 in ascending order by number: 1, 2, 3, 4, 6, and 12.

Negative numbers are included in factors of 12. All of the positive factors of 12 can therefore be changed into negative numbers. Below is a list of the negative factors of 12.

Negative factors of 12 are -1, -2, -3, -4, -6, and -12.

How Many Factors of 12 Are There?

We discovered that 12 had six positives and six negative factors when we added up the factors we described above. Consequently, there are 12 Factors of 12 in all.

Factors of 12 by Prime Factorization

The prime factorization of 12 is given as:

2 x 2 x 3 

First, keep in mind that all positive integers considered to be prime numbers may only be divided equally by one and by oneself. All prime numbers that when multiplied together, equal 12, are known as prime factors of 12.

Prime Factorization of 12 is the process of locating the prime factors of 12. You must divide 12 by the smallest prime number feasible to obtain the prime factors of 12. The next step is to divide the outcome by the smallest prime integer. Continue doing this until you have 1.
The arithmetic to demonstrate the factorization of 12 is as follows:

\[ \frac{12} {2} =  6\]

\[ \frac{6} {2} =  3\]

\[ \frac{3} {3} = 1\]

Once more, the prime factors of 12 are all the prime numbers you used to divide above. 

The prime factorization of 12 is shown below in Figure 1:

Prime factorization of twelve

Figure 2 – Prime factorization of 12

How Many Prime Factors Are There in 12?

We discover that 12 has a total of 3 prime factors when we tally the number of prime factors mentioned above.

Factor Tree of 12

The factor tree of 12 is given below in Figure 2:

Factor tree of twelve

Figure 3 – Factor tree of 12

The representation of a factor of a number specifically obtained via prime factorization is a factor tree. Each branch of the tree grows to create the factors until there is no more room for factorization. There is always a prime number at the branch’s tip.

Factors of 12 in Pairs

A factor pair of 12 consists of two factors that, when multiplied together give 12 as a result. The two integers that can be multiplied together to produce 12 are referred to as the factors, and the number 12 is referred to as the product of these two factors in basic mathematics.

We must first obtain all of the factors of 12 before we can calculate the factor pairs of 12. 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.

As we are aware of every factor that contributes to the number 12, we can utilize this knowledge to determine the factor pairings. To do this, we may search through the list of possible combinations to multiply with each other to find all the possible combinations of 12.

12 x 1 = 12 

6 x 2 = 12 

4 x 3 = 12 

3 x 4 = 12 

2 x 6 = 12 

1 x 12 = 12 

Factors of 12 include negative values, as we mentioned earlier. You may convert the list of positive factor pairs above to negative factor pairs of 12 by simply adding a minus sign in front of each factor. Minus times minus becomes positive.

The positive pair factors for 12 are (12, 1), (6, 2), and (4, 3).

The negative pair factors of 12 are (-12, -1), (-6, -2), and (-4, -3).

Factors of 12 Solved Examples

Example 1

Find the even numbers in the factors of 12.

Solution

Let’s first examine the factors of 12 to get the proportion of even numbers in those components. Below is a list of 12’s factors:

Factors of 12 = 1, 2, 3, 4, 6, and 12

All the factors of 12 are even numbers except 1 so therefore factors of 12 include 5 even numbers.

Example 2

What are the common factors between 12 and 512?

Solution

First, list factors of 12 and 512.

The list of all factors of 12 is 1, 2, 3, 4, 6, and 12 and the factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, and 512.

Now identify the factors shared by both 12 and 512; these will be common factors between 12 and 512.

Therefore, 1, 2, and 4 are the common factors between 12 and 512.

Example 3

Find the greatest common factor between 12 and 500.

Solution

First, list factors of 12 and 500.

The list of all factors of 12 is 1, 2, 3, 4, 6, and 12 and the factors of 500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, and 500.

The common factors between 500 and 12 are 1, 2, and 4 and from these, the greater common factor is 4.

Therefore, the greatest common factor between 12 and 500 is 4.

Images/mathematical drawings are created with GeoGebra.

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