Greatest Common Factor (GCF)

GCF

Introduction

GCF is also known as HCF, the highest common factor is very important in life.

where we use GCF in real life

• To split things into smaller sections?
• To equally distribute 2 or more sets of items into their largest grouping?
• To arrange something into rows or groups?

What is GCF

The greatest factor that divides 2 or more numbers.

Factor:

a factor is a number we can multiply to get the product.

2 x 3 =6→multiple
↓    ↓
factors

Finding GCF

method 1: common division method

find GCF of 12,42

1. first, write the numbers like shown below
   
2. find the  smallest common prime factor that divides both the numbers
   
3. Repeat step 2 until a number can’t divide both numbers.
   

now multiply divisors.

method 2: Prime factorization method

1. First, we have to prime factorize the numbers given(12,42) with the factor tree.
   the factor tree is branch kind which shows all the factors of a number.
   
   Remember: you stop branching the number when the factor is prime like below
    

   

2. then we have the prime factors of 12,42
   12 = 2,2,3
   42 = 2,3,7
   choose the common factors (2,3) then multiply to get the GCF
   GCF=2X3 = 6

Finding GCF by listing Method

Finding GCF by ‘listing method’ is the most common & basic way of finding GCF.

1. list all the factors of the number given(12,42)
   12=1,2,3,4,6,12
   42=1, 2, 3, 6, 7, 14, 21, 42
2. sort out the common factors in both the lists
   common factors of 12,42=1,2,3,6
3. Now sort out the greater number out of the common factor list, and the greatest number will be the GCF
   common factors of 12,42=1,2,3,6←greatest number of all the list
   so…
   GCF=6