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

Prime number, Prime number A prime number is a number whose only +ve fa...

Prime number A prime number is a number whose only +ve factors are 1 and itself. For instance 2, 3, 5, and 7 are all of the examples of prime numbers.  Examples of numbers whic

Integration, why we study integration..?? uses

why we study integration..?? uses

., Two boys A and B are at two diametrically opposite points on a circle. A...

Two boys A and B are at two diametrically opposite points on a circle. At one instant the two start running on the circle; A anticlockwise with constant speed v and B clockwise wit

What is the average of his four quiz grades, Andy earned the subsequent gra...

Andy earned the subsequent grades on his four math quizzes: 97, 78, 84, and 86. What is the average of his four quiz grades? To ?nd out the average, you must add the items (97

Complex numbers, find the modulus Z=(2-i)(5+i12)/(1+i2)^3

find the modulus Z=(2-i)(5+i12)/(1+i2)^3

Nonhomogeneous systems, We now require addressing nonhomogeneous systems in...

We now require addressing nonhomogeneous systems in brief. Both of the methods which we looked at back in the second order differential equations section can also be used now.  Sin

Multiples, The sum of the smallest and largest multiples of 8 up to 60 is?

The sum of the smallest and largest multiples of 8 up to 60 is?

Activities to develop ability to classify, Let us now look at some activiti...

Let us now look at some activities that can be organised with preschoolers to develop their ability to classify. 1. You could start by giving children different materials to pla

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