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GCF Calculator (Greatest Common Factor) HCF,GCD

Enter the values and select the method, and the calculator will determine the Greatest Common Factor (GCF).

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GCF Calculator

The GCF calculator is a simple and reliable tool that determines the greatest common factor of two or more integers. It supports multiple calculation methods and can also display step-by-step solutions for the Greatest Common Divisor (GCD), Highest Common Factor (HCF), or Highest Common Divisor (HCD).

What is the Greatest Common Factor (GCF)?

“The Greatest Common Factor (GCF) is the largest positive number that divides two or more integers exactly, without leaving any remainder.”

The GCF is also commonly referred to as:

Greatest Common Divisor (GCD)
Greatest Common Denominator (GCD)
Highest Common Factor (HCF)
Highest Common Divisor (HCD)

Methods to Calculate the GCF

You can calculate the GCF using several proven mathematical techniques. Below are the most widely used methods:

1. GCF by Listing All Factors

“Write down all factors of each number and identify the greatest factor that appears in every list.”

Example: Find the GCF of 8, 12, and 16.

Factors of 8 = 1, 2, 4, 8
Factors of 12 = 1, 2, 3, 4, 6, 12
Factors of 16 = 1, 2, 4, 8, 16

Common factors = 1, 2, 4 → GCF = 4

2. GCF by Prime Factorization

“Break each number into its prime factors, then multiply the common prime factors using the smallest exponent.”

Example: Find the GCF of 24, 36, and 60.

24 = 2³ × 3
36 = 2² × 3²
60 = 2² × 3 × 5

Common prime factors with smallest powers = 2² × 3 → GCF = 12

3. GCF Using the Euclidean Algorithm

“Apply the formula GCF(a, b) = GCF(b, a mod b) repeatedly until the remainder becomes zero. The last non-zero remainder is the GCF.”

Example: Find the GCF of 48 and 18.

48 ÷ 18 = remainder 12
18 ÷ 12 = remainder 6
12 ÷ 6 = remainder 0

GCF = 6

4. GCF by Binary (Stein’s) Algorithm

“Stein’s Algorithm calculates the GCF using binary operations such as division by 2, subtraction, and comparisons for improved efficiency.”

Arrange the numbers in ascending order.
Initialize a variable for the common power of 2.
Divide all even numbers by 2.
Replace larger numbers with the difference between numbers.
Repeat the process until one number remains.
Multiply the remaining number by the stored power of 2.

Example: Find the GCF of 28 and 20.

Both numbers are even → divide by 2 → 14, 10
Both still even → divide by 2 → 7, 5
(7 − 5) = 2 → divide by 2 → 1
Repeat until equal → result = 1
Multiply by common factor 2² → 4

GCF = 4

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