Introduction to largest common factor

Introduction to largest common factor: 
    
               In mathematics, the largest common factor, also known as the greatest common denominator, greatest common factor (gcf), or highest common factor (hcf), of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder.
              The example and practice problems are given below which will help you to learn finding largest common factor.

Example Problems on Largest Common Factor:

Example 1:

Find the largest common factor of 8 and 14.

Solution:

      Step 1: Find the factors of 8

                        We can divide 8 by 1 or 2 or 4 or 8, so

                                    Factors of 8 = 1, 2, 4, 8

      Step 2: Find the factors of 14

                        We can divide 14 by 1 or 2 or 7 or 14, so

                                    Factors of 14 = 1, 2, 7,14

      Step 3: Find the common factors of 8 and 14

                              Common factors of 8 and 14 = 1, 2

                    Here, 2 is greater than 1. So, 2 is the greatest common factor

      Step 4: Solution

                          Largest common factor of 8 and 14 is 2

Example 2:

Find the largest common factor of 9 and 27.

Solution:

      Step 1: Find the factors of 9

                        We can divide 9 by 1 or 3 or 9, so

                                    Factors of 9 = 1, 3, 9

      Step 2: Find the factors of 27

                        We can divide 27 by 1 or 3 or 9 or 27, so

                                    Factors of 27 = 1, 3, 9, 27

      Step 3: Find the common factors of 9 and 27

                              Common factors of 9 and 27 = 1, 3, 9

                    Here, 9 is greater than 1 and 3. So, 9 is the greatest common factor

      Step 4: Solution

                          Largest common factor of 9 and 27 is 9

Example 3:

Find the largest common factor of 15 and 35.

Solution:

      Step 1: Find the factors of 15

                        We can divide 15 by 1 or 5 or 15, so

                                    Factors of 15 = 1, 5, 15

      Step 2: Find the factors of 35

                        We can divide 35 by 1 or 5 or 7 or 35, so

                                    Factors of 35 = 1, 5, 7, 35

      Step 3: Find the common factors of 15 and 35

                              Common factors of 15 and 35 = 1, 5

                    Here, 5 is greater than 1. So, 5 is the greatest common factor

      Step 4: Solution

                          Largest common factor of 15 and 35 is 5

Practice Problems on Largest Common Factor:

1) Find the largest common factor of 6 and 16.

2) Find the largest common factor of 18 and 24.

3) Find the largest common factor of 12 and 56.

Solutions:

1) Largest common factor of 6 and 16 is 2

2) Largest common factor of 18 and 24 is 6

3) Largest common factor of 12 and 56 is 4.