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**Greatest Common Divisor**

**Greatest Common Divisor -**Greates Common Divisor (

**GCD**), also known as the

**greatest common factor**(

**gcf**) or

**highest common factor**(

**hcf**).

**What is Factor ?**

Factor is a number that can divide other numbers depleted numbers. For more details you can read this example.

Factors of 20: 1, 2, 4, 5, 10, 20

Numbers 1, 2, 4, 5, 10, and 20 is a factor of 20. Why ? Because of these numbers can divide out the number 20.

**What is Greatest Common Divisor ?**

**After we know what that factor ? Then we will understand the meaning of**

__Greatest__

__Common__

__Divisor__. Greatest Common Divisor

**involve at least 2 numbers. Then what is**

**gcd**? Greates common divisor is the greatest number that can divide two numbers are depleted. For more Details you can further reading this post.

**how gcd of 20 and 25 ?**

**For answer the question above**

**maticschool**have some way to answering the questions above.

Some Way .....

1. First way. In this first way we will find the gcd by finding factors of both numbers.

20 : 1, 2, 4, 5, 10, 20

25 : 1, 5, 25

Remember ! What is GCD ? Gcd is the greatest number that can divide both numbers are depleted. From a factor of 20 and 25 can be seen that there are several factors that have in common.

20 : 1, 2, 4, 5, 10, 20

25 : 1, 5, 25

From these data it can be seen that the numbers 1 and 5 are both owned by 20 and 25, but Gcd is the

**greatest**number that can divide two numbers are depleted. So from these data it can be concluded that the gcd is**5.**However, using such means will be relatively very long to find the gcd of two large numbers.
2. Second Way. The second way we will use the relative does not take much time. In second way we will use factor tree for find the gcd. Still with the same problem we will solve this second way.

From factor tree can be concluded :

25 : 52 | 20 : 22, 5

From the above results there are two numbers that equal the number 5, but with different values. Because there are two numbers are the same, we take the smallest value of the 5 factors of 20. Because it only has 1 factor are the same so that's the answer is

**5**

for proof of the second way you can click here

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