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

How to join as maths expert, Sir, I am a Maths teacher from kolkata,India....

Sir, I am a Maths teacher from kolkata,India.i want to join your website as Maths'' expert.Please guide me as to how to join your website and earn some money. I will be really grat

Rational numbers, Although the set of integers caters to a larger aud...

Although the set of integers caters to a larger audience, it is inadequate. This inadequacy has led to the formulation of Rational numbers. Rational numbers are of

Complex number, a ,b,c are complex numbers such that a/1-b=b/1-c=c-1-a=k.fi...

a ,b,c are complex numbers such that a/1-b=b/1-c=c-1-a=k.find the value of k

MAT201, #There is a balance of $1,234 and this person receive a refund chec...

#There is a balance of $1,234 and this person receive a refund check in the amount of $25 with her paycheck that was deposited into her account for $1500 which made her balance $27

Houghton Mifflin math book 3rd grade, i need help with classifing quadrilat...

i need help with classifing quadrilaterals

Compound interest, some experts estimate that the cost of education in the ...

some experts estimate that the cost of education in the US increases by 6% p.a. An Ivy League college currently costs $24,502 for one year''s study today. Using compound interest r

Prove the parallelogram circumscribing a circle is rhombus, Prove that the ...

Prove that the parallelogram circumscribing a circle is rhombus. Ans Given : ABCD is a parallelogram circumscribing a circle. To prove : - ABCD is a rhombus or AB

The fisher’s index, The Fisher's index The index of Fisher acts as a c...

The Fisher's index The index of Fisher acts as a compromise between Paasche' index and Laspeyre's index. This is calculated as a geometric mean of the two indexes.

Unite Ratet, How does finding the unit rate help make smart decisions?

How does finding the unit rate help make smart decisions?

Algebraic models, Establish appropriate algebraic models for each of the fo...

Establish appropriate algebraic models for each of the following sets of data. You can use technology to assist. Plot them on grids and demonstrate how you have established each mo

Write Your Message!

Name

Email id

Message

Verfication Code

User Account

All Pages