There are three methods to find the greatest common factor: multiple method, coprime method and short division.

First, multiple methods

When two numbers have a multiple relationship, the greatest common factor is the smaller of the two numbers. For example, 18 and 9 can directly judge that their greatest common factor is 9, because 18 and 9 have a multiple relationship, 9 is a factor of 18, and 9 is also a factor of 9, that is, 9 is the greatest common factor of 18 and 9.

Second, the coprime method

When two numbers are coprime, their greatest common factor is 1. For example, the greatest common factor of 8 and 9 is 1, because the factor of 8 is 1, 2,4,8. The factor of 9 is 1, 3, 9. Then the common factor of 8 and 9 is only 1, which is the greatest common factor.

So only two numbers whose common factor is 1 are called prime numbers, and the greatest common factor of two numbers is 1. 13 and15; 2 1 and 8? 3 and 5; The numbers 16 1 and 3 are coprime, so their greatest common factor is 1.

Third, short division.

For two numbers that are not in a special relationship, the two numbers with the largest common factor cannot be directly judged, and short division can be used. Take two numbers as dividend and divide by the same number at the same time. The number divided is called divisor. The divisor should be divisible by two numbers at the same time. In fact, this divisor is the factor of two numbers until it can no longer be divided. At this time, the result of multiplying all divisors is the greatest common factor of two numbers.

The benefits of studying mathematics are as follows:

1. Mathematics can make your brain smarter and increase the rigor of thinking.

2. Mathematics is a basic subject. If you can't learn math well, you can't learn anything well. No matter what you want to learn, you must have a foundation in mathematics.

3. Mathematical knowledge runs through our life, which can be said to be everywhere. We live with these mathematical knowledge unconsciously every day.

Mathematics is the study of all quantitative relations and spatial position relations in the world. It can be said that without mathematics, nothing can move.