Greatest Common Divisor
 To enroll in any of our courses, click here

 Greatest Common Divisor (G.C.D.) Greatest Common Factor (GCF) of two numbers is the largest number that divides both of the given numbers exactly. It is called their Greatest Common Divisor (G.C.D.) Follow the following algorithm. Algorithm Step I: Obtain the polynomials. Let the polynomials be p(x) and q(x). Step II: Factorise the polynomials p(x) and q(x). Step III: Express p(x) and q(x) as a product of powers of irreducible factors. Also, express the numerical factor as a product of powers of primes. Setp IV: Identify common irreducible divisors and find the smallest exponents of these common divisors in the given polynomials. Step V: Raise the common irreducible divisors to the smallest exponents found in step IV and multiply them to get the GCD. If there is no common divisor, the GCD is 1.
 People who saw this lesson also found the following lessons useful: Circle: Tangent Circle: Chord Trigonometric Identity Mean of Finite numbers Similar Traingles(Angles are Congruent)
Example: Find the g.c.d. of the following polynomials.
p(x) = 60(3x4 + x3 - 2x2) and q(x) = 10(x6 + 3x5 + 2x4)
Solution: Given
 p(x) = 60(3x4 + x3- 2x2) = 22 * 3 * 5 * x2(3x2 + x - 2) = 22 * 3 * 5 * x2(3x2 + 3x - 2x - 2) = 22 * 3 * 5 * x2[3x(x + 1) - 2(x + 1)] = 22 * 3 * 5 * x2 * (x + 1)(3x - 2) q(x) = 10(x6+ 3x5+ 2x4) = 2 * 5 * x4(x2 + 3x + 2) = 2 * 5 * x4(x2 + 2x + x + 2) = 2 * 5 * x4[x(x + 2) + 1(x + 2)] = 2 * 5 * x4(x + 1)(x + 2)
Here, common irreducible divisors are 2, 5, x and (x + 1). There least exponents are 1, 1, 2 and 1 respectively.
Therefore,
G.C.D. = 2 * 5 * x2 * (x + 1) = 10x2(x + 1).

 As many of you know, Winpossible's online courses use a unique teaching method where an instructor explains the concepts in any given area to you in his/her own voice and handwriting, just like you see your teacher explain things to you on a blackboard in your classroom. All our courses include teacher's instruction, practice questions as well as end-of-lesson quizzes for practice. You can enroll in any of our online courses by clicking here. The format of Winpossible's online courses is also very suitable for teachers who are using an interactive whiteboard such as Smartboard on Promethean in their classrooms, because the course lessons can be easily displayed on such interactive whiteboards. Volume pricing is available for schools interested in our online courses. For more information, please contact us at educators@winpossible.com.

 Copyright © Winpossible, 2010 - 2011 Best viewed in 1024x768 & IE 5.0 or later version