LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

HIGHEST COMMON FACTOR (HCF)

**Highest
Common Factors (HCF)**

**The greatest
number which is a common factor of two or more numbers is their Highest common
factors (HCF) or Greatest Common Divisor (GCD) **

**Example –**

**The factors
of 36 = 3 , 2, 4, 9, 12, 6, 18**

**The factors
of 120 = 2, 3, 4, 5, 6, 8, 10, 12, 15, 24,
60, 40, 30, 20**

**The common
factors of 36 & 120 is 2, 3, 4, 6, 12 and of these 12 is the Greatest
Common Divisor (GCD) or Highest Common Factor (HCF) **

**So, the HCF
of 36 & 120 is 12**

**For your
information, there are two types of methods
of finding HCF –**

**1) By Prime
Factorization method,**

**2) By Division
method**

**There are
step by step methods of finding HCF by Prime Factorization methods are given
below for better understanding –**

**Step.1) Express each Number as a product of prime
numbers **

**Step.2) Find the common factors of the numbers **

**Step.3) Find the product of the common factors, this
product is the required HCF**

**Example.) Find the HCF of 120, 180, 160**

**Answer) 120 = 2 X 60 = 2 X 3 X 20 **

** = 2 X 3 X 2 X 10 **

** =
2 X 3 X 2 X 2 X 5**

** 160 = 2 X 80 = 2 X 2 X 40 **

** = 2
X 2 X 2 X 20 **

** = 2 X 2 X 2 X 2 X 10 **

** = 2 X
2 X 2 X 2 X 2 X 5**

** 180 = 2 X 90 = 2 X 2 X 45 **

** = 2
X 2 X 3 X 15 **

** = 2 X 2 X 3 X 3 X 5**

**The common
factors of 120, 160 & 180 is 2, 2, 5**

**So the
desired HCF is = 2 X 2 X 5 = 20**

**There are
step by step methods of finding HCF by Division methods are given below for
better understanding –**

**Step.1) We
have to divide the bigger number ( consider as Dividend ) by the smaller number
( consider as Divisor ).**

**Step.2) If
there is no reminder then the smaller number is the HCF. If there is a
reminder, take it as the new divisor and take the previous divisor as the new
dividend.**

**Step.3) we
have to continue Step.2 till there is no remainder, the last divisor is the
required HCF.**

**Now, to find
the HCF of three or more numbers, take the following steps –**

**Step.1) Find
the HCF of any two of the numbers**

**Step.2) Find
the HCF of the third number and the HCF obtained in Step.1 **

**This is the
HCF of the three numbers, we have to continue similarly for more given numbers.
**

**Example.)
find the HCF of the following 48, 120 & 216 by division method**

**Answer) As per the given condition, we have to find
the HCF of the tree numbers 48, 120, & 216**

**In three
numbers 48, 120, & 216 here the smallest number is 48 and the biggest number
is 216, so we will consider 48 as divisor and 216 as dividend**

** 48 ) 216 ( 4**

** 192**

** ----------**

** 24 ) 48 ( 2 **

** 48**

** ----------**

** 0**

**Here HCF of 48 & 216 is 24. Now we will
consider obtained result 24 as the divisor and will consider 120 as a dividend which
is the rest number from the given three numbers. **

** 24 ) 120 ( 5**

** 120**

** -----------**

** 0**

**As we can observe that, here HCF of
the 24 & 120 is 24**

**Hence, the HCF of
the three given number is 24 (Ans.)**