Find the prime factorization of each number
List the common prime factors
Take the lowest power of each common prime factor
Multiply those common prime factors with their lowest powers
The product is the HCF
Alternatively, use the Euclidean algorithm for two numbers
Divide the larger number by the smaller number
Replace the larger number with the smaller number and the smaller number with the remainder
Repeat until the remainder is 0
The last non-zero remainder is the HCF