# Vedic Mathematics Techniques for Finding HCF

### Vedic Maths Trick to find the HCF of Algebraic Expressions

To appreciate the Vedic Maths process of finding the HCF you first need to know the other methods taught in school. I am giving you two other methods to compare with.

Example 1: Find the H.C.F. of x^2 + 5x + 4 and x^2 + 7x + 6.

1. Factorization method:
x^2 + 5x + 4 = (x + 4) (x + 1)
x^2 + 7x + 6 = (x + 6) (x + 1)
H.C.F. is ( x + 1 ).
2. Continuous division process.
x^2 + 5x + 4 ) x^2 + 7x + 6 ( 1
x^2 + 5x + 4
___________
2x + 2 ) x^2 + 5x + 4 ( ½x
x^2 + x
__________
4x + 4 ) 2x + 2 ( ½
2x + 2
______
0
Thus 4x + 4 i.e., ( x + 1 ) is H.C.F.

Example 1: Find the H.C.F. of x^2 + 5x + 4 and x^2 + 7x + 6.

1. Factorization method:x^2 + 5x + 4 = (x + 4) (x + 1)

x^2 + 7x + 6 = (x + 6) (x + 1)

H.C.F. is ( x + 1 ).

2. Continuous division process.

x^2 + 5x + 4 ) x^2 + 7x + 6 ( 1

x^2 + 5x + 4___________2x + 2 ) x^2 + 5x + 4 ( ½x

x^2 + x__________4x + 4 ) 2x + 2 ( ½2x + 2______0
Thus 4x + 4 i.e., ( x + 1 ) is H.C.F.

Now see Vedic Maths way of finding HCF of 2 algebraic expressions.

i.e. x+1 is the HCF

Isn’t it much simpler than the above 2 methods.

Now see some more examples –

#### Vineet Patawari

Hi, I'm Vineet Patawari. I fell in love with numbers after being scared of them for quite some time. Now, I'm here to make you feel comfortable with numbers and help you get rid of Math Phobia!

## 6 thoughts to “Vedic Mathematics Techniques for Finding HCF”

1. Vilas Thakur says:

In example no. 2 . -1) 2x + 3 . If we take -1 is common factor from -2x + 3 we get 2x – 3 as a H.C.F. Please let me know am I correct or not . As I have solved the ex. by Factorization and Continuous Division Method . Please let me know the correct answer .

2. its very much interesting.i think its more easy m,ethod for calculation

3. mustafa says:

finding h.c.f of numbers with variables how can be done

4. Anupma Gupta says:

this is in ref to Ex -2

______
-1) -2x +3
_______
2x -3
please see if what I’m trying to point out is correct !!

5. Angle Coomes says:

I’ve just stumbled upon your site while searching for a tutorial on an related subject. Glad I did too. There’s a lot I like. Anyway, you’ve been bookmarked and I’ll be back soon. 🙂

6. Thanks for the nice trick. I feel it will be useful for me in CAT Preparation. Do others agree