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Factors

# Factors of 54 | Prime Factorization of 54 | Factor Tree of 54

Written by Prerit Jain

Updated on: 12 Aug 2023

### Factors of 54 | Prime Factorization of 54 | Factor Tree of 54

Factors of 54: Factors are a series of integers that can divide a given number evenly. Every number has a set of such factors.

There are a total of 8 factors for the number 54. Factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.

The factors of 54 can be positive or negative. These factors can also be written in pairs. So, if we multiply the numbers within the pairs, we will get a product that equals 54.

In this article, we will examine the factors of 54 and the various methods to find them- the division method, prime factorization method, and factor tree method. Keep reading to know more.

## What Are the Factors of 54?

The factors of 54 are the numbers that divide the number (54) evenly without leaving any remainder. The factors of a number can be both positive and negative. Hence, the number 48 has both positive and negative factors.

## What Are the Factors of 54 in Pairs?

A pair factor of 54 is a set of two numbers, that will yield 54 as the product when multiplied. These pair factors can be written in pair format. They can also be written as positive and negative integers.

### Positive Pair Factors of 54

Positive pair factors of 54: (1, 54); (2, 27); (3, 18) and (6, 9).

### Negative Pair Factors of 54

Negative pair factors of 54: (-1, -54); (-2, -27); (-3, -18) and (-6, -9).

## How To Find Factors of 54 Through Division Method?

We will first use the division method to find the factors of 54. As per this approach, we will multiply 54 with a sequence of natural numbers. The numbers that can divide 54 evenly, without leaving reminders are its factors. The steps below give a detailed account of how to find the factors of 54 using the division method.

• 54 ÷ 1 = 54
• 54 ÷ 2 = 27
• 54 ÷ 3 = 18
• 54 ÷ 18 = 3
• 54 ÷ 27 = 2
• 54 ÷ 54 = 1

We can see that the numbers which do not leave any remainder when divided by 54 are 1, 2, 3, 6, 9, 18, 27, and 54. Thus, they are the factors of 54.

## What Is the Prime Factorization of 54?

Before we use the prime factorization method, we must first check if the given number is a prime/ composite number. If the number is a prime number, it has only two factors: 1 and 54. If not, it has more than two factors.

We know that 54 is the composite number so, it has more than two factors. We can use the prime factorization method to find its factors.

The steps to find prime factors of 54 using prime factorization are below:

Step 1: Divide 54 by the smallest prime number that can divide it. That number is 2.
54 ÷ 2 = 27

Step 2: Now, divide 27 by the smallest prime number, which is 3.
27 ÷ 3 = 9

Step 3: Divide the quotient by 3 repeatedly until you get the number prime number as the quotient.
9 ÷ 3 = 3

Step 4: Now we got 3 as the quotient. Dividing 3 with 3 gives us 1.
3 ÷ 3 = 1

The quotient is 1. Since 1 cannot be divided further, the prime factors of 54 are 3 X 3 X 3 X 2 or 33 X 2. We can also write it down as 2 and 3, as both of them are prime numbers.

Image representation of the prime factorization of 54:

## What is the Factor Tree of 54?

Let’s now use the factor tree method to find the factors of 54. As per this method, we will place 54 on top of the factor tree. We will branch it out with one of its pair factors. These pair factors are separated until all branches of the factor tree contain prime numbers.

Step 1: Let’s place the number 54 at the top of the factor tree. We will now branch it out into one of its pair factors- 2 and 27.

Step 2: Since 2 is a prime number, we can no longer separate it. We will now divide 27 into 3 and 9.

Step 3: As we can see, 3 is a prime number but 9 is not, so we will split 9 into 3 and 3.

Step 4: We can see that 2 and 3 are both prime numbers. The branches in the factor tree will now be all the prime numbers.

Hence, circling all the branches, 3 X 3 X 3 X 2 or 33 X 2 = 54, which are 54 prime factors.

Below is an image representation of the factor tree of 54, choosing 3 and 27 as pair factors of 54.

## Factors of 54 Pattern

The pattern that we observe from the factors of 54 is explained below:
Factors of 54 = 1, 2, 3, 6, 9, 18, 27, and 54
From the above, it is clear that every second number is double the first. Let’s write them in pairs to simplify it.

(1, 2); (3, 6); (9, 18) and (27, 54)

## Solved Examples of Factors of 54

Here are some solved examples of 54 factors:

What is the sum of all the factors of 54?
1, 2, 3, 6, 9, 18, 27, and 54 are the 54 factors.
1 + 2 + 3 + 6 + 9 + 18 + 27 + 54 = 120
Hence, 120 is the sum of all 54 factors.

What are the factors and prime factors of 54?
The factors of 54: 1, 2, 3, 6, 9, 18, 27, and 54.
The prime factors of 54: 3 X 3 X 3 X 2 or 33 X 2.

What’s the highest common factor between 54 and 72?
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.
Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.
Hence, from the above, the common factors of 54 and 72 are 1, 2, 3, 4, 6, 9 and 18.
The highest common factor between 54 and 72 is 18.

What’s the highest common factor between 54 and 42?
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.
Factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.
Hence, from the above, the common factors of 54 and 42 are 1, 2, 3, and 6.
The highest common factor between 54 and 42 is 6.

Is 27 a factor of 54?
Yes, 27 is a factor of 54.
As 54 ÷ 2 = 27.

What are the factors of -54?
The factors of -54 are -1, -2, -3, -6, -9, -18, -27, and -54.

What are the common factors of 80 and 54?
To find the common factors of 80 and 54, we need to find the factors of both numbers.
Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80
Factors of 54: 1, 2, 3, 6, 9, 18, 27 and 54
Hence the common factors of 80 and 54 are 1 and 2.

What are all the factors of 54?
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.

What are the factors of 54 that are composite?
Any number which has more than 2 factors is known as a composite number.
The list of number which has more than 2 factors in factors of 54 is 6, 9, 18, 27, and 54.

What factors of 54 are multiples of 2?
The factors of 54 that are multiples of 2 are 2, 6, 18, and 54.
2 x 1 = 2
2 x 3 = 6
2 x 9 = 18
2 x 27 = 54.

How many 54 factors are odd?
A total of 2 odd numbers are there in factors of 54 and they are 1, 3, 9, and 27.

What are the factors of 54 and 36?
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

What are the common factors of 54 and 45?
To list out the common factors of 54 and 45, we need to find the factors of both numbers.
Factors of 54: 1, 2, 3, 6, 9, 18, 27, and 54
Factors of 45: 1, 3, 5, 9, 15, and 45.
From the above, the common factors of 54 and 45 are 1, 3, 9.

How many different factors are there for the number 54?
A total of 8 factors are there for the number 54 and they are 1, 2, 3, 6, 9, 18, 27, and 54.

What factors of 54 are multiples of 3?
The factors of 54 that are multiples of 3 are 3, 6, 9, 18, 27, and 54.

How many pair factors are there in 54?
A total of 4 pairs are there in factors of 54.

What is the largest factor of 54?
The largest factor of 54 is 54.
The second largest factor of 54 is 37.

## FAQs on Factors of 54

List all the factors of 54
1, 2, 3, 6, 9, 18, 27, and 54 are the 54 factors.

What are the composite factors of 54?
6, 9, 18, 27, and 54 are the 54 composite factors.
Composite factors are those that have more than 2 factors other than 1 and itself.

What are the factors of 54 in pairs?
(1, 54), (2, 27), (3, 18) and (6, 9) are the 54 factors of pairs.

What are the positive factors for 54?
1, 2, 3, 6, 9, 18, 27, and 54 are the positive factors for 54.

List the negative pairs of 54
The negative pairs of 54: (-1, -54), (-2, -27), (-3, -18) and (-6, -9)

Now that you have all the necessary information regarding the factors of 54, We hope this blog has been useful for you and easy to understand as well.

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Prerit Jain

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