**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 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**

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.