1, the greatest common divisor, also known as the greatest common factor and greatest common divisor, is a mathematical concept, which refers to the greatest common divisor between two or more integers.
2. The methods to solve the greatest common divisor include prime factor decomposition, short division, phase division and phase subtraction, and the corresponding concept is the least common multiple.
3, short division to find the greatest common divisor, first divide by the common divisor of these numbers until all the quotients are coprime, and then multiply all the divisors to get the product that is the greatest common divisor of these numbers.
4. Short division is to write the prime factor shared by two numbers where the divisor is written in the division, then put down the quotient of two numbers divisible by the common prime factor, divide it again, and so on until the result is coprime (two numbers are coprime).
Expansion of the greatest common divisor;
1, first appeared in geometric primitive people (about 300 BC). In volume 7, it is used for integers, and in volume 10, it is used for line segment length (that is, it is called real number now, but there was no concept of real number at that time).
2. Among several methods to solve the greatest common divisor, the most famous one is division by tossing and turning. Commutation division is one of the oldest algorithms still in use.
3. The algorithm in volume 10 is geometric, and the greatest common divisor of two sections A and B is to accurately measure the maximum length of A and B. ..
4. This algorithm may not have been invented by Euclid, but just compiled the achievements of our ancestors into his geometric primitives. Mathematician and historian Vander Waals Deng thinks that the content of Volume 7 may come from a textbook of number theory written by a mathematician in Pythagoras College.