## Finding HCF of expressions using Vedic Mathematics

**Highest Common Factor (HCF)** as the name suggests it is the highest common factor present between 2 or more expressions or numbers For Example: HCF of 8 and 10 is 2. While that of 8 and 12 is 4 and so on. In this topic we are going to see the HCF of expressions. Calculation of HCF can be done in following ways:

- Adyamadyena Rule to find the factors of the expression and name the common factor/s as the HCF.
- Lopanasthapana Method by elimination and retention method or Sankalana-Vyavakalana Process which means addition and subtraction to eliminate and retain the highest power of dependent term.

We will be using 2nd way.

Examples:

Find HCF of x^{2} + 7x + 6 and x^{2} -5x -6

So HCF = x+1

Find HCF of 4x^{3} + 13x^{2} + 19x + 4 and 2x^{3} + 5x^{2} + 5x -4

While subtraction we multiplied eq 2 by 2 and done subtracted from eq1 for elimination x^{3} term.

So HCF = x^{2}+ 3x + 4

Find HCF of x^{4}+ x^{3} -5x^{2}– 3x+2 and x^{4}-3x^{3}+x^{2}+3x-2

So HCF = x^{2}-x-2

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