To find the Highest Common Factor i.e. H.C.F. of algebraic expressions, the
factorization method and process of continuous division are in practice in the
conventional system. We now apply' Lopana - Sthapana' Sutra, the 'Sankalana
vyavakalanakam' process and the 'Adyamadya' rule to find out the H.C.F in a
more easy and elegant way.
Question: Find the H.C.F. of x2 + 5x + 4 and x2 + 7x + 6.
1. Factorization method:
x2 + 5x + 4 = (x + 4) (x + 1)
x2 + 7x + 6 = (x + 6) (x + 1)
H.C.F. is ( x + 1 ).
2. Continuous division process.
x2 + 5x + 4) x2 + 7x + 6 ( 1
x2+ 5x + 4
2x + 2 ) x2 + 5x + 4 ( ½x
4x + 4) 2x + 2 ( ½
2x + 2
Thus 4x + 4 i.e., ( x + 1 ) is H.C.F.
destruction of the highest and the lowest powers is as below:
i.e.,, (x + 1) is H.C.F