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:
Find prime factors of both numbers
Break down each number into its prime factors
Identify common prime factors
Find the prime factors that appear in both factorizations
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
Method 2: Euclidean Algorithm
Efficient for larger numbers
Step-by-Step Process:
Divide larger by smaller number
Divide and note the remainder
Divide divisor by remainder
Replace dividend with divisor and divisor with remainder
Repeat until remainder is 0
The last non-zero remainder is the HCF
Example: HCF of 60 and 48
Divide 60 (larger) by 48 (smaller):
60 ÷ 48 = 1 with remainder 12
So: 60 = 48 × 1 + 12
Divide 48 (previous divisor) by 12 (remainder):
48 ÷ 12 = 4 with remainder 0
So: 48 = 12 × 4 + 0
Remainder is 0, so HCF is the last divisor:
The last non-zero remainder was 12
Example of Using the HCF Calculator
Let's say you want to find the HCF of 12, 18, and 24.
- Enter 12, 18, 24 (separated by a comma or space).
- Click Calculate HCF.
- The result will show 6 because 6 is the largest number that divides all three numbers evenly.
Why is HCF Important?
- Simplifies fractions easily
- Helps solve division and arithmetic problems
- Identifies common divisors of numbers
- Useful in real-life grouping and distribution problems
How Does the HCF Calculator Work?
- Enter two or more numbers in the input field
- Click the Calculate HCF button
- The calculator instantly displays the HCF result
FAQ on HCF Calculator
HCF (Highest Common Factor) is the largest number that divides two or more numbers exactly without leaving a remainder.
The Euclidean algorithm is the fastest and easiest way to find HCF, especially for large numbers.
Yes, HCF and GCD (Greatest Common Divisor) mean the same thing and are used interchangeably.
No, the HCF is always less than or equal to the smallest of the given numbers.
Yes, HCF can be calculated for two or more numbers by repeatedly finding the HCF of pairs of numbers.