1. Finding HCF (2 numbers)
Ladder method

2. Recap-Common Factors
Common Factors are factors common to all given numbers
Find common factors of 12 and 16
• The factors of 12 are: 1 , 2 , 3 , 4 , 6 and 12
• The factors of 16 are: 1 , 2 , 4 , 8 and 16
So the common factors of 12 and 16 are: 1 , 2 and 4

3. Highest Common Factor
Definition: The Highest Common Factor (HCF) of two or more given numbers is the highest (or greatest) of their common factors. It is also known as Greatest Common Divisor (GCD). Example: Find the Highest Common Factor(HCF) of 12 and 16. Factors of 12 : 1, 2, 3, 4, 6, 12 Factors of 16: 1, 2, 4, 8, 16 The common factors of 12 and 16 are 1 , 2 and 4 Highest Common Factor(HCF) will be the highest of the given common factors – i.e. 4 Therefore HCF of 12 and 16 is 4.

4. Facts
1. HCF of Co-prime numbers is 1 , since they will not have any factors other than 1
Example : HCF of 6 and 35 is 1, since they do not have any common factors other than 1
HCF of two different prime numbers is 1 , since they do not have any common factors
other than 1
Example : HCF of 5 and 11 is 1

5. Finding HCF by Ladder Method
Step 1: Divide the given numbers by their common factor other than 1 Step 2: Continue dividing till the only common factor left to divide is 1 Step 3: HCF is the product of all the common factors

6. 2 6 , 12 3 , 6 3 1 , 2 Example 1: Find the HCF of 6 and 12 Solution:
Step 1: Divide the given numbers by
their common factor other than 1
Step 2: Continue dividing till the only
common factor left to divide is 1
Step 3: HCF is product of all the common factors
HCF (6 , 12) = 6
Ans: 6
6 , 12
3 , 6
1 , 2 2 3
Common
Factors
There is no common
factor left other than 1 to divide so we stop here
HCF = 2 x 3 = 6

7. 13 13 , 39 1 , 3 Example 2: Find the HCF of 13 and 39 Solution:
Step 1: Divide the given numbers by
their common factor other than 1
Step 2: Continue dividing till the only
common factor left to divide is 1
(in this case there is no need for this step so we stop)
Step 2: HCF is product of all the common factors
HCF (13 , 39) = 13
Ans: 13
Common
Factor
, 39
1 , 3 13
There is no common
factor left other than 1 to divide so we stop here
HCF = 13

8. 2 36 , 48 18 , 24 3 9 , 12 3 , 4 Example 3: Find the HCF of 36 and 48
Solution:
Step 1: Divide the given numbers by
their common factor other than 1
Step 2: Continue dividing till the only
common factor left to divide is 1
Step 3: HCF is product of all the common factors
HCF (36 , 48) = 12
Ans: 12
, 48
18 , 24
9 , 12 2 3
3 , 4
Common
Factors
There is no common
factor left other than 1 to divide so we stop here
HCF = 2 x 2 x 3 = 12

9. 14 , 27 Example 4: Find the HCF of 14 and 27 Solution:
Step 1: Divide the given numbers by
their common factor other than 1
HCF of two numbers that does not have a common factor is 1
HCF (14 , 27) = 1
Ans: 1
No Common Factors
, 27

10. Try these
1. Find the highest common factor of 15 and 25? 2. Find the highest common factor of 18 and 72? 3. Find highest common factor of 21 and 35?