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

Complex numbers, 1+2i=a+ib so find a and b

1+2i=a+ib so find a and b

Plus, 1+1

1+1

The number of filtering steps, The amount of particulate matter left in sol...

The amount of particulate matter left in solution during a filtering process is given by the equation p(n) = 500(2) -0.8n , where n is the number of filtering steps. Find the amoun

Example of addition of fractions, Example of addition of Fractions: 10...

Example of addition of Fractions: 105/64 + 15/32 + 1/6 =____ would require the denominator to be equal to 64 x 32 x 6 = 12,288. This type of number is very hard to use.

Shares and divident, A man invest ?13500 partly in shares paying 6% at ?140...

A man invest ?13500 partly in shares paying 6% at ?140 and partly in 5% at 125.If he is tolal income is 560, how much has he invested in each?

Differential equations, do you help with Calculus AB AP homework?

do you help with Calculus AB AP homework?

Laplace transform, what is the Laplace transform of e^9(-t)^a)

what is the Laplace transform of e^9(-t)^a)

Pre-operational stage-development learning maths, Pre-operational Stage : ...

Pre-operational Stage : This period of a child's cognitive development usually begins at the age of 2, and lasts until about the age of 6. Thus, it usually coincides with the pre

Probability, Mike sells on the average 15 newspapers per week (Monday – Fri...

Mike sells on the average 15 newspapers per week (Monday – Friday). Find the probability that 2.1 In a given week he will sell all the newspapers

Shoppers` stop, 3. How are Indian customers visiting Shoppers’ Stop any dif...

3. How are Indian customers visiting Shoppers’ Stop any different from customers of developed western countries? 4. How should Shoppers’ Stop develop its demand forecasts?

Write Your Message!

Name

Email id

Message

Verfication Code

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!

Submit Assignment

User Account

All Pages