List the numbers
Find the factors of each number
Identify the common factors
Select the greatest common factor
The greatest common factor is the highest common factor
For larger numbers, use prime factorization
Write each number as a product of prime factors
Identify the common prime factors
Multiply the common prime factors
The result is the highest common factor
For two numbers, use the Euclidean algorithm
Divide the larger number by the smaller number
Replace the larger number with the smaller number
Replace the smaller number with the remainder
Repeat until the remainder is 0
The last non-zero remainder is the highest common factor