Greatest Comman divisor and Eulers formual

1. Greatest Common
Divisor - GCD
and Euclidean Algorithm

2. Definition
• The GCD is the greatest number that divides a set of numbers
without leaving a remainder. For example: GCD of 4 and 6 is
2, as it divides both numbers and is the largest of all their
factors.
• The GCD of any two numbers is never negative or 0, and the
least positive integer common to any two numbers is always
1.

7. Example

8. Algorithm of finding GCD

9. Example

10. Methods to Find GCD
• Prime Factorization Method
• Euclid’s Division Algorithm
• Binary GCD Algorithm (Stein's Algorithm)

11. Prime Factorization Method to Find GCD

13. Euclid’s Division Algorithm

15. Binary GCD Algorithm (Stein's
Algorithm)

17. Euclidean algorithms
• The Euclidean Division Algorithm is a method used in
mathematics to find the greatest common divisor (GCD) of
two integers. It is based on Euclid's Division Lemma. In this
algorithm, we repeatedly divide and find remainders until
the remainder becomes zero.

18. Euclid Division Lemma

23. Pseudocode of GCD