Question

Find the hcf of 336,54 and express the hcf as 336 *x+54*y

Answer 1

$\large{\underline{\bf{Solution-}}}$

By Using Euclid's division lemma,

a = bq + r

=> 336 = (54×6) + 12.............(1)

=> 54 = (12×4) + 6..............(2)

=> 12 = (6×2) + 0

HCF = 6

_____________________________

From 1)

6 = 54 - (12×4)...........(3)

From 2)

12 = 336 - (54 × 0)............(4)

Put the value of (4) in (3)

6 = 54 - [336-(54×6)] × 4

=> 54 - (4×336) + 54 × 24

=> (54×25) + (-4)(336)

$\therefore$ x = -4 and y = 25

Answer 2

THEORY USED : EUCLID’s DIVISION LEMMA

A = BQ + R , where 0<_ r < B