Greatest common divisor
![A 24-by-60 rectangle is covered with ten 12-by-12 square tiles, where 12 is the GCD of 24 and 60. More generally, an a-by-b rectangle can be covered with square tiles of side length c only if c is a common divisor of a and b.](/Images/godic/202501/16/24x60.svg0005.png")
![](/Images/godic/202501/16/Least_common_multiple.svg0005.png")
![Animation showing an application of the Euclidean Algorithm to find the Great Common Divisor of 62 and 36 which is 2.](/Images/godic/202501/16/-The_Great_Common_Divisor_of_62_and_36_is_2.ogv0005.jpg")
![](/Images/godic/202501/16/Greatest_common_divisor0005.png")
In mathematics, the greatest common divisor (gcd) of two or more integers, when at least one of them is not zero, is the largest positive integer that divides the numbers without a remainder. For example, the GCD of 8 and 12 is 4.
The greatest common divisor is also known as the greatest common factor (gcf), highest common factor (hcf), greatest common measure (gcm), or highest common divisor.