Greatest Common Factor: Simple Method, Factorial and Example Problem

The greatest common divisor - of two numbers is the largest positive integer that can evenly divide the two numbers, the following is a complete explanation of the greatest common factor which includes how to find the common factor in a simple way and factorial. For more details, see the discussion below

The greatest common divisor

The greatest common factor (GCF) of two numbers is the largest positive integer that is able to evenly divide the two numbers by themselves

Example

A simple method can be used to find the greatest common factor of 2 or 3 numbers that are not too large, but for larger numbers you should use the factorial method.

Simple way

Finding the Greatest Common Factor of 12 and 20:

The factors of 12 are 1, 2, 3, 4, 6 and 12
Factors of 20 are 1, 2, 4, 5, 10 and 20
The Greatest Common Factor of 12 and 20 of the largest (same) allied factors, which is 4.

Finding the Greatest Common Factor of 15 and 25:

Factors of 15 are 1, 3, 5′, and 15
Factors of 25 are 1, 5, and 25
The greatest common factor of 15 and 25 is the largest (same) allied factor, which is 5.

Factorial way

Finding the Greatest Common Factor of the numbers 147, 189 and 231:

Create a factor tree for each number:

Arrange the numbers from the factor tree to get their factorial values:

The factorial of 147 is 31 x 72
The factorial of 189 is 33 x 71
Factorial 231 = 31 x 71 x 111

• Take the factors whose allies are the same from the three factorials, namely 3 and 7.
• Multiply the common factor that has the smallest power, which is 31 x 71 = 21.

Then the greatest common factor of the numbers 147, 189 and 231 is 21. In other words, no number greater than 21 can evenly divide the numbers 147, 189 and 231.

How to find the greatest common factor with prime factorization

This method is a quick way to calculate the Greatest Common Factor. The factor tree is used to find a prime factor. Based on these prime factors, then calculate the Greatest Common Factor of the requested number. There is a procedure for calculating the Greatest Common Factor with a factor tree that can be done as follows:

1. Create all factor trees of numbers
2. Take all the factors that are the same from each factor of the number. In this case apply the set operations needed to find the greatest common factor
3. Multiply the numbers into the Greatest Common Factor

Example of the Largest Common Factor

Example Question 1

What is the greatest common factor of 6 and 9 ?

Answer:

Factors of 6 are 1, 2, 3, 6
Factors of 9 are 1, 3, 9

Notice that the same largest number of factors 6 and 9 is 3.

Example Question 2

What is the greatest common factor of 8, 12, and 20?

Answer:

Factors of 8 are 1, 2, 4, 8
Factors of 12 are 1, 2, 3, 4, 6, 12
Factors of 20 are 1, 2, 4, 5, 10, 20

Example Question 3

Find the greatest common factor of 16 and 20!

Answer

The first step

The factors of 16 are 1, 2, 4, 8, and 16

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

Step 2

The common factors of 16 and 20 are 1, 2, and 4

Step 3

The greatest common factor of 16 and 20 is 4

That's the discussion about the greatest common factor along with examples of the problem, Hopefully it's useful

Other Articles:

• Complete Double Angle Formula With Example Problems
• Related Angle Formulas: Quadrant Formulas 1, 2, 3, 4 and Example Problems
• The formula for the base of a triangle along with the formula for height and example questions
• Spherical Surface Area Formula and Example Problems Contoh
• Definition, Properties, Quadratic Equation Formulas and Example Problems