HCF Calculator

Enter numbers separated by spaces or commas (e.g., 12, 18 24)

What is an HCF Calculator?

The Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), is a mathematical term used to describe the largest number that divides two or more integers without leaving a remainder. For the example, the HCF of 40 and 60 is 20 because 20 is the largest number that can divide both 40 and 60 evenly. An HCF Calculator is a tool designed to help you quickly find the HCF of two or more numbers. Whether you are solving math problems, simplifying fractions, or dealing with other number calculations, an HCF calculator is an essential tool to have on hand.

How to do HCF step by step?

To find the HCF (Highest Common Factor) of two numbers step by step, you can use two main methods:

Method 1: Prime Factorization

Best for smaller numbers

Step-by-Step Process:

1
Find prime factors of both numbers

Break down each number into its prime factors

2
Identify common prime factors

Find the prime factors that appear in both factorizations

3
Multiply common prime factors

Use the lowest power of each common prime factor

Example: HCF of 60 and 48

Step 1: Prime Factors

60 = 2 × 2 × 3 × 5 (2² × 3 × 5)

48 = 2 × 2 × 2 × 2 × 3 (2⁴ × 3)

Step 2: Common Prime Factors

Common primes: 2 and 3

Minimum powers: min(2², 2⁴) = 2² = 4 and min(3¹, 3¹) = 3

Step 3: Multiply common factors

HCF = 2² × 3 = 4 × 3 = 12

HCF(60, 48) = 12

Method 2: Euclidean Algorithm

Efficient for larger numbers

Step-by-Step Process:

1
Divide larger by smaller number

Divide and note the remainder

2
Divide divisor by remainder

Replace dividend with divisor and divisor with remainder

3
Repeat until remainder is 0

The last non-zero remainder is the HCF

Example: HCF of 60 and 48

1

Divide 60 (larger) by 48 (smaller):

60 ÷ 48 = 1 with remainder 12

So: 60 = 48 × 1 + 12

2

Divide 48 (previous divisor) by 12 (remainder):

48 ÷ 12 = 4 with remainder 0

So: 48 = 12 × 4 + 0

3

Remainder is 0, so HCF is the last divisor:

The last non-zero remainder was 12

HCF(60, 48) = 12

How Does the HCF Calculator Work?

The HCF Calculator works by finding the largest number that divides all the entered numbers without leaving a remainder. Here's how the calculator typically works:

Input the Numbers

Enter the numbers you want to find the HCF for. You can enter the numbers separated by spaces or commas (e.g., 12, 18, 24, 39).

Click Calculate

After entering the numbers, click the "Calculate HCF" button to let the tool process the input.

Get the Result

The calculator will then display the Highest Common Factor (HCF) of the numbers you entered.

Why is the HCF Important?

The HCF is useful in various aspects of mathematics and real-world applications. Here are a few reasons why the HCF is important:

Simplifying Fractions

When simplifying fractions, The HCF is used to divide the numerator and denominator to find the simplest form of the fraction.

Solving Arithmetic Problems

The HCF is also important when solving problems related to division and finding common multiples.

Finding Common Divisors

The HCF helps identify common divisors of two or more numbers, which is useful in number theory and other advanced mathematical concepts.

Real-World Applications

The HCF can also be used in real-world problems like distributing items into groups, such as dividing objects into equal parts for an event.

How to Use the HCF Calculator?

Step 1

Enter the numbers you want to find the HCF for in the input field. You can enter numbers separated by either commas or spaces.

Step 2

Click the "Calculate HCF" button to initiate the calculation.

Step 3

The calculator will show you the HCF of the entered numbers. You can use this result to simplify fractions, solve math problems, or understand the relationships between the numbers.

Example of Using the HCF Calculator

Let's say you want to find the HCF of 12, 18, and 24.

  1. Enter 12, 18, 24 (separated by a comma or space).
  2. Click Calculate HCF.
  3. The result will show 6 because 6 is the largest number that divides all three numbers evenly.
This video explains how to calculate HCF using our free HCF calculator. Watch the steps and try it yourself using the tool below.

Benefits of Using an HCF Calculator

Fast and Accurate

The calculator provides instant results, saving you time and effort in manual calculations.

Easy to Use

The user interface is simple and easy to navigate, making it accessible to both students and professionals.

Flexible Input

You can enter numbers separated by spaces or commas, which makes it more convenient for various input styles.

No Complex Formulas

The calculator eliminates the need for manually applying division rules or complex algorithms to find the HCF.