Solution: Because 6÷2=3, 3÷3= 1. ?

And 9 ÷ 3 = 3,3 ÷ 3 =1.

Through the short division of the numbers 6 and 9, we can know that the prime factor of 6 and 9 is 3. ?

So the greatest common factor of 6 and 9 is 3. ?

Extended data:

1, the properties of the factor

(1) A number is divisible by all the factors of this number.

For example, if the factors of 4 are 1,-1, 2, -2, 4 and -4, then 4 can be divisible by any of these factors.

(2) A number is a prime number if only two positive integers are its factors.

Example: 3= 1x3=3x 1, 5= 1x5=5x 1, then 3 is a prime number and 5 is a prime number.

2. Solving the greatest common factor

(1) short division?

Find the greatest common divisor by short division. First, use the common divisor of these numbers to continuously remove until all the merchants are coprime, and then put all

The divisor multiplied by is the greatest common divisor of these numbers.

For example: 8 ÷ 2 = 4,4 ÷ 2 = 2,2 ÷ 2 =1

6÷2=3,3÷3= 1

Because the common divisor of 8 and 6 is only 2, the greatest common divisor of 8 and 6 is 2.

(2) prime factor decomposition method

First, several numbers are decomposed into prime factors, and then all the common prime factors in each number are taken out and multiplied, and the products obtained are these numbers.

The greatest common divisor of.

For example:12 = 2x3x3, 18=2x3x3.

Because the prime factors of 12 and 18 are 2 and 3, the greatest common factor of 12 and 18 is 2x3=6.

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