Greatest common factor (GCF)

There are differents way to find the GCF of numbers.

Look at them and choose the one you prefer!!!

##

Method 1

First list all of the factors of each number, then list the

**common factors** and choose the largest one.

**Method 1**

Find the GCF of 12 and 36
The factors of 12 are

**1, 2, 3, 4, 6** and

**12**.

The factors of 36 are

**1, 2, 3, 4, 6**, 9,

**12**, 18 and 36.

The **common factors** of 12 and 36 are **1, 2, 3, 4, 6 and 12**

Although the numbers in **bold** are all common factors of both 12 and 36, 12 is the **greatest common factor**.

##

Method 2

To find the GCF of a set of numbers, you must factor each of the numbers into primes. Then for each different prime number in all of the factorizations, do the following...

1. Count the number of times each prime number appears in all the factorizations.

2. For each prime number, take the lowest of these counts and write the result.

3. The greatest common factor is the product of all the prime numbers written down.

*Example*: GCF (4,6)=2, because 4=2·2 and 6=2·3, so GCF(4,6)=2

If GCF(a,b)=1, is said that a and b are

**relative primes**

**Method 2**

**Find GCF(72,90,120)**

1. Determine the prime factorization of each number:

72=2^{3}·3^{2}

90=2·3^{2}·5

120=2^{3}·3·5

2. Take the prime numbers that appears in all the factorizations. (Remember taking the lowest number of times they appear)

Prime numbers selected: 2 y 3

3. GCF(72,90,120)=2·3=6