# Factors of 54

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

#### How to find factors of a number

 1.   Find factors of 54 using Division Method 2.   Find factors of 54 using Prime Factorization 3.   Find factors of 54 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 54

• Divide 54 by 1: 54 ÷ 1 : Remainder = 0
• Divide 54 by 2: 54 ÷ 2 : Remainder = 0
• Divide 54 by 3: 54 ÷ 3 : Remainder = 0
• Divide 54 by 6: 54 ÷ 6 : Remainder = 0
• Divide 54 by 9: 54 ÷ 9 : Remainder = 0
• Divide 54 by 18: 54 ÷ 18 : Remainder = 0
• Divide 54 by 27: 54 ÷ 27 : Remainder = 0
• Divide 54 by 54: 54 ÷ 54 : Remainder = 0

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

#### 2. Steps to find factors of 54 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 54 using the division method, follow these steps:

• Step 1. Start dividing 54 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 54, which is 2. Divide 54 by 2 to obtain the quotient (27).
54 ÷ 2 = 27
• Step 3. Repeat step 1 with the obtained quotient (27).
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1

So, the prime factorization of 54 is, 54 = 2 x 3 x 3 x 3.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 54 as shown below:

So, the prime factorization of 54 is, 54 = 2 x 3 x 3 x 3.

#### 3. Find factors of 54 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 54 would be the two numbers which, when multiplied, give 54 as the result.

The following table represents the calculation of factors of 54 in pairs:

Factor Pair Pair Factorization
1 and 54 1 x 54 = 54
2 and 27 2 x 27 = 54
3 and 18 3 x 18 = 54
6 and 9 6 x 9 = 54

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 54. They are called negative pair factors.

Hence, the negative pairs of 54 would be ( -1 , -54 ) , ( -2 , -27 ) , ( -3 , -18 ) and ( -6 , -9 ) .

#### How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 54 is a factor of itself.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 3, 6, 9, 18, 27, 54 are exact divisors of 54.
• 1 is a factor of every number. Eg. 1 is a factor of 54.
• Every number is a factor of zero (0), since 54 x 0 = 0.

• Which is the smallest prime factor of 54?

Smallest prime factor of 54 is 2.

• Is 54 a perfect square?

No 54 is not a perfect square.

• What are five multiples of 54?

First five multiples of 54 are 108, 162, 216, 270, 324.

• What is prime factorization of 54?

Prime factorization of 54 is 2 x 3 x 3 x 3.

• What are factors of 54?

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

• How do you find factors of a negative number? ( eg. -54 )?

Factors of -54 are -1, -2, -3, -6, -9, -18, -27, -54.

• Is 54 a whole number?

Yes 54 is a whole number.

• Which is greatest factor of 54?

The greatest factor of 54 is 27.

• What are the prime factors of 54?

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

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 54. Can you help her?

Prime factors of 54 are 2, 3, 3, 3.
Hence, the product of prime factors of 6.

Can you help Rubel to find out the product of the even factors of 54?

Factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54.
Even factors of 54 are 2, 6, 18, 54.
Hence, product of even factors of 54 is; 2 x 6 x 18 x 54 = 11664.

Joy wants to calculate mean of all the factors of 54. Help him in finding the mean of 54.

Factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 54 is 1 + 2 + 3 + 6 + 9 + 18 + 27 + 54 = 120.
Hence, the mean of factors of 54 is 120 ÷ 8 = 15.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 54? Help her in writing all the factors.

Positive factors are 1, 2, 3, 6, 9, 18, 27, 54.
Negative factors are -1, -2, -3, -6, -9, -18, -27, -54.

How many factors are there for 54?

Factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54.
So there are in total 8 factors.

Joey wants to write all the prime factors of 54 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 54 are 2, 3, 3, 3.
So in exponential form it can be written as 2 x 33.

Kevin has been asked to write 7 factor(s) of 54. Can you predict the answer?

7 factor(s) of 54 are 1, 2, 3, 6, 9, 18, 27.