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.

Posted Date: 4/8/2013 1:00:56 AM | Location : United States

Ask an Expert

Related Discussions:- Express the gcd as a linear combination, Assignment Help, Ask Question on Express the gcd as a linear combination, Get Answer, Expert's Help, Express the gcd as a linear combination Discussions

Write discussion on Express the gcd as a linear combination
Your posts are moderated

Write your message here..

Related Questions

Geometry, Determine the coordinates of the point equidistant from Salt Lake... Determine the coordinates of the point equidistant from Salt Lake City and Helena

Compute simple addition, John was doing his homework on vertical addition, ... John was doing his homework on vertical addition, and had to compute : 5 3+ 3 4  and 6 8 +45 He did the first one easily, just the way his teacher had taught him. He first ad

Fundamental methods of mathematical economics, manual for this book manual for this book

The null hypothesis, The null hypothesis It is the hypothesis being tes... The null hypothesis It is the hypothesis being tested, the belief of a specific characteristic for illustration, US Bureau of Standards may walk to a sugar making company along

Using substitution in equation, i dont know how to do it i dont know how to do it

Finite difference method, Two reservoirs of equal cross sectional areas (31... Two reservoirs of equal cross sectional areas (315 m 2 ) and at equal elevations are connected by a pipe of length 20 m and cross sectional area 3 m 2 . The reservoir on the left (

Sqares, Recently I had an insight regarding the difference between squares ... Recently I had an insight regarding the difference between squares of sequential whole numbers and the sum of those two whole numbers. I quickly realized the following: x + (x+1)

What is the probability in which the marble chosen is blue, A bag holds 3 r... A bag holds 3 red, 6 blue, 5 purple, and 2 orange marbles. One marble is selected at random. What is the probability in which the marble chosen is blue? The probability of blue

Decimals to fractions, change 5.075 to a fraction change 5.075 to a fraction

Demerits and merit-the geometric mean , The geometric mean Merits ... The geometric mean Merits i.  This makes use of all the values described except while x = 0 or negative ii.   This is the best measure for industrial increase rates