Question

H.C.F (81,234)=81x+234yfind x and y

Answer 1

Step-by-step explanation:

Given HCF of the numbers 81 and 234 i.e H.C.F (81,234)=81x+234y

we have to find the value of x and y

By Euclid 's Division Algorithm,

Hence, HCF is 3

Given 3 = 81x + 237y for some x and y.

From step 3

3 = 75 - 6(12)

3 = 75 - ( 81 - 75)(12)

3 = 75 - (81×12 - 75×12)

3 = 75 - 81×12 + 75×12

3 = 75 (13) - 81(12)

3 = (237 - 81×2)(13) - 81(12)

3 = 237(13) - 81(38)

3 = 237(13) + 81(-38)

which is in the form 237x + 81y = 3

Therefore, x = 13 , y = - 38.

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