Question

Find the HCF by Euclid of 336 and 54 if D = 336 X + 54 Y find X and Y

Answer 1

✤SOLUTION✤

●Using Euclid's division algorithm

➹336 = 54 × 6 + 12 _____eqn(2)

➹54 = 12 × 4 + 6 ___eqn(1)

➹12 = 6 × 2 + 0

Here we get

HCF(336, 54) =6

By eqn(1)

6 = 54 - 12 × 4

By eqn(2)

12 = 336 - 54 × 6

Putting eqn(2) in place of 12 in eqn(1)

We get,

6 = 54 - ( 336 - 54 × 6 ) × 4

6 = 54 - [ 336 (4) - 54 × 6 × (4) ]

6 = 54 - 336 (4) + 54 × (24)

6 = 54 + 54 (24) - 336 (4)

6= 54( 1 + 24 ) + 336 × (- 4)

6= 54 (25) + 336 (- 4)

●comparing with

D = 336 X + 54 Y

We get,

X = - 4

Y= 25

When D = 6 , that is the HCF of 336 and 54.

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