In the context of mathematics, the greatest common divisor represents the largest number by which two or more numbers can be divided. If all the factors of two or more numbers are found and you find that some factors are the same (“Common”), then the greatest of these common factors is the Greatest Common Divisor. Abbreviated as "MCD". To find out which are the numbers that divide them, there are two ways: the long way and the shortest way.
The most direct way is to extract from all the numbers that they pose us, their divisors. The highest repeating divisor in all the questioned numbers is the GCF
For example: GCF (20, 10)
Divisors of 20: 1, 2, 4, 5, 10 and 20
10: 1, 2, 5 and 10 separators
The highest common divisor for both is 10, and therefore their GCF is 10.
The aforementioned system can only be used in small numbers, because it is simple, but it becomes complicated for high numbers, there are more comfortable systems.
The factor decomposition system is the most common and used method. It is about breaking down each number that you ask us into all its divisors. After performing this step, you must take the common factors with the lowest exponent and multiply them between them.
Therefore, what you do is decompose the numbers by prime factors. Common factors that have a lower exponent are taken and then these factors are multiplied. The result is the GCF. The other two paths are Euclid's algorithm or the least common multiple.
One of the applications of the greatest common divisor is to simplify fractions. To simplify it, the GCF of each number is usually calculated, dividing the numerators and denominators of the fraction by the result of the GCF, thus obtaining a simplified fraction. For example, in the following fraction: 48/60.
The greatest common factor of 48 and 60, previously extracted by a common factor, is 12. Therefore, we divide 48 by 12 (4). And 60 by 12 (5). The simplified fraction will be 4/5.
