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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.

Related Calculators
Calculate Greatest Common Factor Common Factor Calculator
Calculate least Common Multiple Common Denominator Calculator
 

Example Problems on Largest Common Factor:

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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:

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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.


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