CLASS-4
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,