LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

HIGHEST COMMON FACTOR (HCF)

__HIGHEST COMMON FACTOR (H.C.F) OR GREATEST COMMON DIVISOR
(G.C.D) –__

**The H.C.F or G.C.D of
two or more numbers is the greatest number that divides each one of them
exactly-**

**If we consider the
number 24 and 36 then,**

** the factors of
the 24 are = 1, 2, 3, 4, 8, 6, 12, 24**

**the factors of
the 36 are = 1, 2, 3, 4, 6, 9, 12, 18, 36 **

** so, common
factors of the 24 and 36 are = 1, 2, 3, 4, 6, 12 and the greatest between these
is 12**

**So, H.C.F or G.C.D of
the two given numbers 24 & 36 is 12. (Ans.)**

__ANOTHER METHOD OF – FINDING H.C.F THROUGH PRIME FACTORISATION
METHOD –__

**Find the H.C.F of 24 & 36**

**Step.1)****
Express each number which is to be considered as a product of prime factors.**

__Step.2)__ Find the common factors to
all the numbers.

**Step.3)****
The product of these common factors is the required H.C.F**

** 24 = 2 x
2 x 2 x 3 x 1**

**36 = 2
x 2 x 3 x 3 x 1**

**The common factors of
the given numbers are 2, 2, & 3.**

**So, H.C.F of 24 &
36 is = 2 x 2 x 3 = 12 (Ans.)**

__ANOTHER METHOD OF – FINDING H.C.F THROUGH LONG DIVISION METHOD –__

**1) Find H.C.F of 120
and 576 by Long Division Method**

**Ans.) For finding the
H.C.F of two given numbers by long division method, we should proceed according
to the following steps are given below –**

__Step.1)__**
Consider the greater number as ‘Dividend’ and smaller number as ‘
Divisor’, so, consider 576 as ‘Dividend’ and 120 as ‘Divisor’.**

__Step.2)__** Start division like normal division and you will find the remainder
every time, and then again we have to divide ‘Divisor’ by
‘Remainder’. Here 96 is ‘Remainder’ and 120 is ‘Divisor’, as per the
given communication we will divide 120 by 96 and the steps continue.**

** Step.3) Continue
step 2 until the ‘Remainder’ becomes 0 (Zero). The last ‘Divisor’ is the
desired H.C.F, so 24 is the H.C.F of both the numbers 120 & 576.**

__H.C.F OF THREE OR MORE NUMBERS –__

**1) Find H.C.F of 120,
576, and 444 by Long Division Method**

**Ans.) For finding the
H.C.F of two given numbers by long division method, we should proceed according
to the following steps are given below –**

__Step.1)__**
Find H.C.F of any two of the given numbers and then find H.C.F of the
third given number and the H.C.F number obtained from first two numbers.**

__Step.2)__** Take
two numbers 120 & 576, consider the greater number as ‘Dividend’ and the smaller
number as ‘ Divisor’, so, consider 576 as ‘Dividend’ and 120 as
‘Divisor’.**

__Step.3)__** Start division like normal division and you will find the remainder
every time, and then again we have to divide ‘Divisor’ by ‘Remainder’.
Here 96 is ‘Remainder’ and 120 is ‘Divisor’, as per the given
communication we will divide 120 by 96 and the steps continue.**

__Step.4)____ __Continue
step 2 until the ‘Remainder’ becomes 0 (Zero). The last ‘Divisor’ is the
desired H.C.F, so 24 is the H.C.F of both the numbers 120 & 576.

__Step.5)__**
Now, we have to find H.C.F through the division method of third
given number 444 and H.C.F 24 obtained from two given numbers 120 & 576.**

** We will
consider 24 as ‘Divisor’ and 444 as ‘Dividend**

__Step.6)__**
we will continue Step.3 & Step.4, process of division method continues
till ‘Remainder’ is 0 (Zero)**

**So, H.C.F of 24
& 444 is 12,**

**So, H.C.F of
given three numbers 120, 576, 444 is 12. (Ans.)**