In this article let us learn what we mean by factor and greatest common factor. Consider 3 x 5 = 15. We could say that 3 and 5 are the factors of 15. When we multiply the factors we get the respective number.

**Finding gcf with example :**

The abbreviation of Greatest common factor is gcf. Before learning about greatest common factor, let us learn about common factor. Let us find the common factor of 25, 100, 125.

Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50 and 100

Factors of 25 are 1, 2, 5 and 25.

Factors of 125 are 1, 5, 25 and 125

Pick up the numbers that occurs in common to all the three numbers. They are 1, 5 and 25.

The greatest numbers among the common factors are called as greatest common factor. According to the above example, 25 is the greatest common factor.

- Using prime factorisation find the prime factors of the given numbers.

- Find the common factors of the given numbers

- Pick the greatest number among the common factors and that is the solution

**Note:** gcf of relatively prime numbers is 1.

**Ex:** 2 and 3 are relatively prime numbers. So, gcf of 2 and 3 is 1.

12 and 13 are relatively prime numbers. So, gcf of 12 and 13 is 1.

**Ex 1: Find the gcf of 26 and 39.**

**Sol:**

**Step 1:** Find the prime factors of 26 and 39.

Prime Factors of 26 are 26 = 2 x 13

Prime Factors of 39 are 39 = 3 x 13.

**Step 2:** Find the common factor and greatest among the common factor.

It is 13

**Step 3:** Write the solution

Gcf of 26 and 39 is 13

**Ex 2: Find the gcf of 121,22 and 55.**

**Sol:**

**Step 1:** Find the prime factors of 121, 22 and 55.

Prime Factors of 121 are 121 = 11 x 11

Prime Factors of 22 are 22 = 2 x 11.

Prime Factors of 55 are 55 = 5 x 11

**Step 2:** Find the common factor and greatest among the common factor.

It is 11

**Step 3:** Write the solution

Gcf of 121, 22 and 55 is 11