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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:

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.

*AP and SAT are registered trademarks of the College Board.