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

Solving whole-number riddles, I am greater than 30 and less than 40. The su...

I am greater than 30 and less than 40. The sum of my digits is less than 5. who am I?

Solve the algebraic equestions, Solve the following equestions i.2x-8=8 ...

Solve the following equestions i.2x-8=8 ii.3x+2/5=4 iii.8/3x-2=2 iv.0.6x-5=7

Kfso, poijn jjjnjb jbjdbjbj

poijn jjjnjb jbjdbjbj

Forced - damped vibrations, It is the full blown case where we consider eve...

It is the full blown case where we consider every final possible force which can act on the system. The differential equation in this case, Mu'' + γu'  + ku = F( t) The displ

Tower of hanoi, how to create an activity of tower of hanoi

how to create an activity of tower of hanoi

Surds and logarithms, what are these all about and could i have some exampl...

what are these all about and could i have some examples of them please

Interpolation and extrapolation, Interpolation is a method of s...

Interpolation is a method of statistical estimation and the word literally means 'making insertions'. Let us consider a well-known situation whi

Logarithmic functions, If x = b y where both b > 0, x > 0, then we d...

If x = b y where both b > 0, x > 0, then we define y = log b x, which is read as "y is the log to the base b of x". This means that, log b x or y is the number to

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