First, the tossing and turning division of labor

Conversion division, also called Euclid algorithm, is a method to find the greatest common factor of two positive integers A and B. The basic idea is: divide a large number by a decimal, and the remainder is 0, then the greatest common factor is a decimal; Otherwise, the decimal and remainder will be substituted into the next operation.

And so on until the remainder is 0 and the last divisor is the greatest common divisor. This method is simple, intuitive, easy to understand and fast in calculation, and is often used in practical problems.

Second, the multiphase loss method

Multiphase subtraction is a method to find the greatest common divisor in ancient China, which is developed on the basis of phase division. The basic idea of more relative subtraction is: a large number MINUS a decimal, if the difference is a decimal, the greatest common divisor is the difference; Otherwise, the sum and difference of large numbers are substituted into the next operation.

And so on, until the difference is 0, the last reduction is the greatest common divisor. This method is slow in calculation, and in some cases there may be an infinite loop, but it has advantages in dealing with some special problems.

Third, enumeration method.

The so-called enumeration method is to enumerate the factors of two numbers separately, then find out their common factors, and finally find out the greatest common factor from the common factors. For example, find the greatest common factor of 6, 15. This method can be used for smaller numbers, but it is not very convenient for larger numbers.

Factor of 6: 1, 2, 3, 6;

15 factor: 1, 3,5,15;

Their common factor is 1, 3;

So their greatest common factor is 3.

Fourth, short division.

Divide these two numbers by their common prime factor until the quotient obtained is coprime (that is, there is no common factor), and then multiply all the divisors (that is, the numbers to the left of the short divisor), and the product is the greatest common factor of these two numbers. This method is the simplest and most commonly used, and it is also convenient to calculate the greatest common factor of a large number.

In practical application, it is necessary to choose appropriate methods according to the characteristics of specific problems, so as to solve problems more efficiently.

In a word, solving the greatest common factor is an important problem in mathematics and daily life. Understand a variety of methods, according to the specific situation to choose the appropriate method to solve.