HCF of 48 and 54

The HCF of 48 and 54 is 6. HCF stands for Highest Common Factor, and as the name suggests, the number that is highest among the common factors is known as HCF. It can also be referred to as GCD, Greatest Common Divisor or GCF, Greatest Common Factor. For the given set of numbers 48 and 54, 6 is the HCF/GCD/GCF. Even though there are other common factors 1, 2, and 3, 6 is greater than the other common factors. You can refer to the HCF and LCM to understand the difference between them.

What is the HCF of 48 and 54?

The Highest Common Factor, also known as the Greatest Common Factor, of 48 and 54 is 6. 

How to Find HCF of 48 and 54?

There are three methods to find the HCF of 48 and 54:

  • Prime Factorisation
  • Long Division method
  • Listing common factors

HCF of 48 and 54 by Prime Factorisation Method

In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 48 and 54 can be expressed as:

48 = 2 × 2 × 2 × 2 × 3 

54 = 2 × 3 × 3 × 3

Common prime factors are 2 and 3. Therefore, HCF will be

HCF (48, 54) = 2 × 3 = 6.

HCF of 48 and 54 by Long Division Method

In the Long Division method, the below steps are followed.

  1. From the given set of numbers, the smallest number becomes the divisor, and the larger number becomes the dividend.
  2. In the next step, the smaller number becomes the dividend, and the remainder becomes the divisor. 
  3. The above step is followed until the remainder is zero. 
  4. The last divisor would be the HCF.

For 48 and 54, the HCF by long division method is:

HCF 30

Hence, HCF (56, 84) = 6

HCF of 48 and 54 by Listing Common Factors

By listing all the factors of given numbers, we can identify the Highest/Greatest/Biggest common factor, which is the HCF. Below is the list of factors for 48 and 54:

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 

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

Therefore, HCF (48, 54) = 6

Related Articles

Video Lesson on Properties of HCF and LCM

Solved Examples

1. Find the second greatest number that divides 48 and 54 evenly.

The common factors of 48 and 54 are 1, 2, 3 and 6. The second greatest number that divides 48 and 54 evenly is 3.

2. What is the GCF of 5 and 5?

The GCF of 5 and 5 is 5.

Frequently Asked Questions on HCF of 48 and 54

Q1

What is the HCF of 48 and 54?

The HCF of 48 and 54 is 6.
Q2

Is the HCF of 48 and 54 the same as the LCM of 48 and 54?

No. The Highest Common Factor of 48 and 54 is 6 and the Least Common Multiple of 48 and 54 is 432.
Q3

What are the common prime factors of 48 and 54?

The common prime factors of 48 and 54 are 2 and 3.
Q4

What are the three common multiples of 48 and 54?

The three common multiples of 48 and 54 are 432, 864 and 1296.
Q5

What are the factors of 48?

The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

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