Euclidean Algorithm for Large Numbers, a Method of Computing GCF, LCM

A method of computing the greatest common factor, GCF (also called the greatest common divisor, GCD, or the highest common factor, HCF) of large numbers


Let's calculate the greatest common factor GCF (the greatest common divisor, GCD, HCF) of the numbers 53,667 and 25,527 by using the Euclid's algorithm:

The greatest common factor GCF (or greatest common divisor, GCD, HCF) of the numbers is the last remainder that is not zero.

Let's calculate the greatest common factor, GCF (greatest common divisor, GCD) of (87; 41) by using Euclid's algorithm:

Why is the answer a factor (a divisor) of the initial 'a' and 'b'?

Why is the answer equal to the CGF (HCF, GCD)?

Euclid's algorithm for more than two numbers:

Euclid's algorithm: find the least common multiple, LCM (also called lowest common multiple, or smallest common factor), of large numbers


Proof for the LCM formula


What is a prime number?

What is a composite number?

Prime numbers up to 1,000

Prime numbers up to 10,000

Sieve of Eratosthenes

Euclid's algorithm

Simplifying ordinary (common) math fractions (reducing to lower terms): steps to follow and examples