Find the greatest common factor instantly — with full step-by-step working
GCF Calculator
Show steps using
Greatest Common Factor
16
Numbers entered
48, 64
Least Common Multiple
192
All common factors of 48, 64
The highlighted chip is the GCF.
Step 1. Find the prime factorization of each number.
Step 2. Identify common prime factors and take the lowest power of each.
Step 3. Multiply the common prime factors:
GCF = 2^4 = 16
The GCF Calculator finds the greatest common factor (also called GCD or HCF) of two or more integers in seconds. Enter your numbers and choose between prime factorization or the Euclidean algorithm to see every step explained clearly. Whether you are simplifying fractions, solving math homework, or working with ratios, this free tool shows the full working so you understand exactly how the answer is reached.
The greatest common factor of two or more integers is the largest positive integer that divides all of them without leaving a remainder. For example, the GCF of 48 and 64 is 16, because 16 is the biggest number that goes evenly into both.
You break each number down into its prime factors, then identify the primes that appear in every number. Multiply the lowest power of each shared prime together to get the GCF. For 48 (2⁴ × 3) and 64 (2⁶), the shared prime is 2 with minimum power 4, so GCF = 2⁴ = 16.
The Euclidean algorithm repeatedly divides the larger number by the smaller one and replaces the larger with the remainder. When the remainder hits 0, the last nonzero remainder is the GCF. It is very efficient for large numbers and is the basis of many computer algorithms.
Yes — enter any quantity of integers separated by commas or spaces. The calculator applies the GCF operation iteratively across all numbers. The step-by-step prime factorization view supports any count, while the Euclidean table is shown only when exactly two numbers are entered.