Question

find HCF of 1656 and 843 and express it as linear combination​

Answer 1

Answer:

Given:

• numbers 1656 and 843

To find:

• The H.C.F and to express it in linear combination.

Solving Question:

We are given the the numbers and are asked to find the H.C.F that we can find it using Euclid's division lemma.The by simple substituting the values we could find answer.

Solution:

To find H.C.F

by Euclid's division lemma,

1656 = 843*1 + 813   .......equ(1)

r ≠ 0 , therefore,

or, 843 = 813 * 1 +30  ........equ(2)

r ≠ 0 , therefore,

or, 813 = 30*27 +3  ..........equ(3)

r ≠ 0 , therefore,

or, 30 = 3*10 + 0  ..........equ(4)

r = 0 , hence the H.C.F is 3

Take Equ(2)

843 = 813 *1 +30

or, 813 = 843 -30 .....equ(5)

Take equ(1)

1656 = 843*1 + 813

substitute equ(5)

or, 1656 = 843*1 + 843 -30

or, 30 = 843(2) - 1656

or, 30 = 843(2) + 1656(-1)

Take 'x' = 2 and 'y' = -1

∴The linear equation is 30 = 843x + 1656y