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HIGHEST COMMON FACTOR (HCF)

__HIGHEST COMMON FACTOR (HCF)__

**EUCLID, a Greek mathematician discovered HCF.**

**HCF is also known as GREATEST COMMON DIVISOR (G.C.D).**

**In
two, three, or more of the given numbers which will be the common highest number
in all given numbers are called Highest Common Factors (HCF).**

**For
an example, suppose there are two numbers that are given one is 25 and another is
15.**

**If we wish to select
HCF from given numbers, first we have to split the both numbers in their
multiplication –**

**25
= 1 x 5 x
5 or all the common factors of 25 are = 1 , 5 ,
25**

**15
= 1 x 3 x 5 or all the common factors of 15 are = 1 , 3 , 5 ,
15**

**In the above numbers we can see that, the common factors are 1 & 5, and 5 is
the highest common factor.**

**So, the Highest Common Factors (HCF) of above two numbers is 5.**

__DIVISIBILITY -__

**Now
we will learn, how to understand which ‘Dividend’ is divisible by which ‘Divisor’.**

**Suppose
there is a number, that is 453 and we have to find which number will be
‘Divisor’,**

**Firstly
add all the digit of 453 like = 4 + 5 + 3 = 12, 12 is divisible by 3.**

__BASIC
FACTORIZATION -__

**Basic
Factorization is nothing but a simplified multiplication form.**

**For
an example, basic factorization of 24 = 1 x 2 x 2 x 2 x 3.**

**basic
factorization of 36 = 1 x 2 x 2 x 3 x 3.**

**a) 1 has only one factor and that is the number (1) itself. It is called ‘Unique‘
number.**

**b)
2, 3, 5, 7, 11, 13 have only two factors, 1 and the number itself, these
numbers are called ‘Prime’ Numbers.**

**c)
Numbers having three or more factor like 4, 6, 8, 10, 12, ……… are called ‘Composite**’ **Number**.

__Highest Common Factor (HCF) By Basic Factorization -__

**1) Find HCF of 15 & 25**

**Ans.)
Factors of 15 = 3, 5, 1, 15**

**
Factors of 25 = 5, 5, 1, 25**

**Common factors of 15
& 25 are 5, 1, so HCF of 15 & 25 is = 5 x 1 = 5 (Ans.)**

**2) Find HCF of 24 & 36.**

**Ans.) Factors
of 24 = 2, 2, 2, 3, 1, 24**

**
Factors of 36 = 3, 2, 2, 3, 1, 36**

** Common factors
of 24 & 36 are 2, 2, 3, 1.**

**So, HCF of 24 &
36 = 2 x 2 x 3 x 1 = 12. (Ans.)**

__HCF by Division Method__

**Example.1) Find HCF of 12 & 24.**

**So, factors of 12 are
= 2 x 2 x 3 x 1**

**
Factors of 24 are = 3 x 2
x 2 x 2 x 1**

**So, common factors
are = 3, 2, 2**

**HCF of 12 & 24
is = 3 x 2 x 2 = 12 (Ans.)**

**Example.2) Find the HCF of 45 & 153.**

**45 = 5 X 3 X 3**

**153 = 17 X 3 X 3**

**So, product of the
common factors = 3 X 3 = 9**

**HCF of 45 & 153
is 9 (Ans.)**

**There are some other way of understanding about H.C.F is given below -**

**1) Common Factor Method Or Listing Method,**

**2) Prime Factorization Method,**

**3) Division Method,**