Express the gcd as a linear combination, Mathematics

Assignment Help:

Express the GCD of 48 and 18 as a linear combination.              (Ans: Not unique)

A=bq+r, where  o ≤  r < b

48=18x2+12

18=12x1+6

12=6x2+0

∴ HCF (18,48) = 6

now  6= 18-12x1

6= 18-(48-18x2)

6= 18-48x1+18x2

6= 18x3-48x1

6= 18x3+48x(-1)

i.e.       6= 18x +48y

∴      x=3 , y=-1

6= 18×3 +48×(-1)

=18×3 +48×(-1) + 18×48-18×48

=18(3+48)+48(-1-18)

=18×51+48×(-19)

6=18x+48y

∴         x = 51, y = -19

Hence, x and y are not unique.


Related Discussions:- Express the gcd as a linear combination

Algorithm for division helping a child grasp, E1) Why don't you think of so...

E1) Why don't you think of some activities for the same purpose now? E2) Suggest, in detail, another activity for helping a child grasp the algorithm for division. We come to

Limit comparison test - sequences and series, Limit Comparison Test Ass...

Limit Comparison Test Assume that we have two series ∑a n and ∑b n with a n , b n   ≥ 0 for all n. Determine, If c is positive (i.e. c > 0 ) and is finite (i.e. c

Determine the domain and range of function, Determine the domain of each of...

Determine the domain of each of the following functions.                         f( x ) = x - 4 / x 2 - 2 x -15 Solution With this problem we have to avoid division by

common divisors greater than one, Let R be the relation on Z + defined by...

Let R be the relation on Z + defined by aRb iff gcd(a; b) = 1 (that is, a and b have no common divisors greater than one). Explain whether R is reflexive, irreflexive, symmetri

MUTIPLYING FRACTIONS, EVERY TIME I TRY TO DO ANY KIND OF FRACTIONS WELL MUL...

EVERY TIME I TRY TO DO ANY KIND OF FRACTIONS WELL MULTIPLYING I ALWAYS GET IT WRONG

Algebra, please tell me what is algebra and how i can understand it

please tell me what is algebra and how i can understand it

Evaluate the limit, Evaluate the given limit. Solution : It is a ...

Evaluate the given limit. Solution : It is a combination of many of the functions listed above and none of the limited are violated so all we have to do is plug in x = 3

Developing estimation skills in maths, DEVELOPING ESTIMATION SKILLS :  A s...

DEVELOPING ESTIMATION SKILLS :  A study was done with some Class 3 and Class 4 children of five village schools to gauge how well they had understood the standard algorithms. The

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd