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Factors of 54: Prime Factorization, Methods, Tree, and Examples

Factors of 54 are an algebraic expression that divides the number 54 evenly such that there are no remainders after the division. The answer we get from such division is always in whole number form and never in the decimal format.

A factor can also be a whole number when divided with another whole number to give the original number as an answer.

The number 54 is an even. Note that every even number can be divided by 2. We can say that 2 is a factor of 54. Since 2 is a factor it also proves that 54 is a composite number. Every composite number has more than two factors i.e. 1 and 54 itself.

The total number of factors of 54 is 16. 8 of these are positive factors, and the rest 8 are negative factors of number 54.

In this article, you will be guided to all of the major concepts related to factors and subcategories like prime factorization, tree, examples, etc. By the end, you will be capable to solve questions related to the factors of 54 on your own.

What Are the Factors of 54?

The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54. A factor of any natural number can divide it completely without leaving any remainders.

As a factor is the exact divisor of the original number so it can never be zero or greater than the number itself. We can say that the factors of 54 are:

Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54 

How To Calculate the Factors of 54?

To calculate the factors of 54 we will follow the following steps:

For the division method you follow these steps:

\[ \dfrac{54}{1}=54, remainder = 0\]

\[ \dfrac{54}{2}=27, remainder = 0\]

\[ \dfrac{54}{3}=18, remainder = 0\]

\[ \dfrac{54}{6}=9, remainder = 0\]

\[ \dfrac{54}{9}=6, remainder = 0\]

\[ \dfrac{54}{18}=3, remainder = 0\]

\[ \dfrac{54}{27}=2, remainder = 0\]

\[ \dfrac{54}{54}=1, remainder = 0\]

Note that after the number 6 the factors will start to repeat themselves.

For the factors of 54, we will start dividing the number with the smallest factor which is 1. 1 is the factor for every single number. Then we will divide 54 with another number which will give us a whole number quotient and zero remainders. We will repeat this process for all consecutive integers from 1 to 54. 

So from the above steps, we can list the factors of 54 as 1, 2, 3, 6, 9, 18, 27, and 54.

By following the same steps we can calculate all of the negative factors of 54 too which are given as follow:

Negative factors of 54 = -1, -2, -3, -6, -9, -18, -27, -54

We can find the factors of 54 by multiplication method.

\[1\times 54 = 54 \]

In this method, we will take any two numbers which are less than 54 and greater than 0. If by multiplying them we get 54 as our answer then we will consider those two numbers will be considered as the factors of 54.

Factors of 54 by Prime Factorization

Prime numbers are the integers that can only be divided by 1 or that number itself. So when prime numbers are multiplied together to give the desired number, we call such prime numbers the prime factors of the original number. This process is called prime factorization.

For the prime factorization of 54 we will follow these steps:

\[ \dfrac{54}{2}=27, remainder = 0\]

\[ \dfrac{27}{3}=9, remainder = 0\]

\[ \dfrac{9}{3}=3, remainder = 0\]

\[ \dfrac{3}{3}=1, remainder = 0\]

To get the Prime factorization of 54 you will divide 54 with the smallest prime number. If the answer is a whole number then we will keep on dividing the answer with that prime number. But if we get a decimal number then we will shift to the next prime number. We will keep on repeating this process until we get 1 answer.

We can write the Prime Factorization of 54 as:

\[ 2\times 3\times 3\times 3 = 54 \]

  

Figure 1

Factor Tree of 54

54 has in total 4 prime factors. Every composite factor has a factor tree. It is a method to graphically analyze the factors of 54.

The factor tree of the number 54 is shown below:

Figure 2

Factors of 54 in Pairs

Factor pairs of 54 can be found by multiplying any 2 factors which give 54 as an answer. The combination of any two factors makes is a factor pair.

We can find the factor pair of 54 as:

\[1\times 54 = 54 \]

\[2\times 27 = 54 \]

\[3\times 18 = 54 \]

\[6\times 9 = 54 \]

We will not repeat the factors so the factor pairs of 54 can be listed as:

(1,54)

(2,27) 

(3,18) 

(6,9) 

As every number has both positive and negative factors so we can also find the negative factor pairs of 54.

\[ -1\times -54 = 54 \]

\[ -2\times -27 = 54 \]

\[ -3\times -18 = 54 \]

\[ -6\times -9 = 54 \]

So we can write the negative factor pairs as:

(-1,-54)

(-2,-27)

(-3,-18)

(-6,-9)

Factors of 54 Solved Examples

Following are some solved examples.

Example 1

Dan is a clerk at a news agency who has to divide a set of 54 paperclips and put them in 3 different sections of the office which are:

  1. The headlines section
  2. The sports section
  3. The weather section

How ill he distribute an equal number of paperclips?

Solution

As we know that the factors of 54 are:

Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54 

As Dan has to divide 54 paperclips into 3 different sets so:

\[ \dfrac{54}{3}=18 \]

So each workstation will get a set of 18 paperclips each.

Example 2

Jeremiah has been asked to find the greatest and smallest factor of the number 54 for his math homework. Help him out.

Solution

The factors of 54 are

Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54

So from this list, we can say that the greatest factor of 54 is 54 itself and the smallest factor is 1.

The greatest Factor of 54 is  54.

The smallest Factor of 54 is 1.

Example 3

Susan makes a knitted sweater in 54 hours in 3 days. How many hours did she use every day to complete her sweater?

Solution

It took Susan 8 days and in total 54 hours to complete a sweater.

We can say that: 

\[ -3\times -18 = 54 \]

So it took 18 hours every day for Susan to complete her sweater.

Images/mathematical drawings are created with GeoGebra.

Factors of 53|Factors list| Factors of 55

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