All factors of 54 include 1, 2, 3, 6, 9, 18, 27 and 54. The factors of 54 are the numbers that can evenly divide 54 leaving no remainder behind. These factors can include both positive and negative integers.

In this article, we will discuss all the topics related to the factors of 54, including all the factors of 54, prime factors of 54, and the factor tree of 54.

What are Factors?

The factor of a number is any number that divides the given number completely without leaving any remainder.

Every positive integer has at least two factors: 1 and the number itself. Examples of factors of a number are:

• Factors of 18: 1, 2, 3, 6, 9, and 18.
• Factors of 29: 1, and 29.

In the case of 54, all the numbers like 1, 2, 3, 6, 9, 18, 27, and 54 are the factors of 54 because they all divide 54 completely without leaving any remainder.

Read More, Factors of a number.

What are Factors of 54?

Factors of 54 are the numbers that can be multiplied together to give the product as 54. For example, product of 2 and 27 gives 54 hence, 2 and 27 are factors of 54. Similarly.

• 1 × 54 = 54
• 2 × 27 = 54
• 3 × 18 = 54
• 6 × 9 = 54

So, Factors of 54 are: 1, 2, 3, 6, 9, 18, 27 and 54.

All Factors of 54

The list of all factors of 54 is:

Factors of 54 : 1, 2, 3, 6, 9, 18, 27 and 54

Prime Factors of 54

Prime factors is a prime number that divides another number without leaving a remainder. List of all factors of 54 include both prime and composite numbers. However, we can also express 54 as the product of only prime numbers. The prime factors of 54 can be determined by dividing 54 by the smallest possible prime number until we get 1.

• 54 ÷ 2 = 27
• 27 ÷ 3 = 9
• 9 ÷ 3 = 3
• 3 ÷ 3 = 1

The numbers 2 x 3 x 3 x 3 that multiply together to give back the number 54, are called the prime factors of 54.

Factors of 54 Calculator

How to Find the Factors of 54?

Factors of a number can be find by the following methods:

• Division Method
• Multiplication Method
• Prime Factorization

Let’s find the factors of 54 by the division method.

Factors of 54 by Division Method

To find the factors of 54 by division method, you can use the hit and trial method to check if a certain number completely divides 54 or not, but before that keep the following things in mind:

• The number 1 and the number itself are always the factors of the given number.
• The factors of a number are always less than the given number.

Now that we know that 1 and 54 are the factors of 54, we can start checking numbers starting from 2. Here are the factors of 54:

• 54 ÷ 2 = 27
• 54 ÷ 3 = 18
• 54 ÷ 6 = 9

The factors of 54 are: 1, 2, 3, 6, 9, 18, 27, and 54.

Prime Factorization of 54

To express 54 as the factor of prime numbers, we use prime factorization. Prime factorization is a process of repeated division such that the divisor each time is only a prime number. For 54, we will follow the following steps:

Step 1: Start with 54.

Step 2: Divide by 2: 54 ÷ 2 = 27

Step 3: Divide by 27: 27 ÷ 3 = 9

Step 4: Divide by 3 : 9 ÷ 3 = 3

Step 5: Divide by 3 : 3 ÷ 3 = 1

You can see here that in each step, we have only used a prime number for division until we completely divide 54. This can be represented as follows:

Hence, the prime factorization of 54 is 2 × 3 × 3 × 3 = 2 × 3³

Also Check, Prime Factorization

Factor Tree of 54

Factor tree is a chart that shows all the prime factors of a number in the form of a tree like diagram, for 54 we can make the factor tree of 54 as follows:

• Begins with the number 54.
• After that, Break 54 into 2 and 27.
• Then, 2 will remain as it is, and 27 will be expanded into 3 and 9.
• At last, only 9 will be expanded into 3 and 3

Below is an illustration of a factor tree of 54.

Factor Pairs of 54

Factor Pairs of 54 are pairs of numbers that gives 54 by multiplying two factors. The factors pairs are the pair of integers which when multiplied together, give the original number back. Any integer number, positive or negative, can be included in the factor pair of a number. The positive and negative factor pairs of 54 are listed below:

Positive Factor Pairs of 54

The positive factor pairs of 54 are:

• 1 × 54 = 54
• 2 x 27 = 54
• 3 x 18 = 54
• 6 x 9 = 54

So, the positive pair factors of 54 are (1, 54), (2, 27), (3, 18), and (6, 9).

Negative Factor Pairs of 54

The negative factor pairs of 54 are:

• (-1) × (-54) = 54
• (-2) × (-27) = 54
• (-3) × (-18) = 54
• (-6) × (-9) = 54

So, the negative pair factors of 54 are (-1, -54), (-2, -27), (-3, -18), and (-6, -9).

Read More,

• Factors of 18
• Factors of 6
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Solved Examples on Factors of 54

Example 1: Find the common factors of 54 and 17.

Solution:

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

Factors of 17 = 1, 17

Thus, the only common factor of 54 and 17 is 1.

Example 2: Is 54 a prime number?

Solution:

The factors of 54 are = 1, 2, 3, 6, 9, 18, 27, and 54.

Since 54 has more than two factors, it is not a prime number.

Example 3: Are factors and multiples of 54 the same?

Solution:

No, the factors of 54 are the numbers smaller than or equal to 54, that completely divide 54 whereas, the multiples are the numbers that come in the table of 54 and are equal to or greater than 54.

Example 4: What is the sum of the factors of 54?

Solution:

The factors of 54 are = 1, 2, 3, 6, 9, 18, 27, and 54.

The sum therefore is, 1 + 2 + 3 + 6 + 9 + 18 + 27 + 54 = 120.

Practice Problems on Factors of 54

Problem 1: What is the greatest prime factor of 54?

Problem 2: What will be the value of a, if a x b = 54 and b = 3?

Problem 3: What is the product of the factors of 54?

Problem 4: Find the common factors of 54 and 84.

Problem 5: Are there any common numbers in the factors and multiples of 54?

Factors of 54: Frequently Asked Questions

List all Factors of 54.

The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.

How do you Find the Factors of 54?

To find the factors of 54, you can divide 54 by various numbers and check which ones result in whole number quotients without remainders.

What is Prime Factorization of 54?

The prime factorization of 54 is 2 × 3 x 3 x 3

How many Factors does 54 have?

The total factors of 54 are 8.

What is Highest Prime Factor of 54?

The prime factors of 54 are 2 x 3 x 3 x 3. Thus, the highest prime factor is 3.

What is Sum of all Factors of 54?

The sum of all the factors of 54 is 120.

Is 54 a Perfect Square?

No, 54 is not a perfect square because it cannot be expressed as the square of an integer.