Question

Use Euclid algorithm to find the HCF of 56 and 72and hence express in the form of 56x + 72y​

Answer 1

Answer:

Step-by-step explanation:

Euclid division algorithm states that, If a and b are two integers,and when a is divided by b, giving Quotient r and remainder p,then it can be written as

a= b p + r,where, 0≤r<b

72=56×1 +16

56=16×3+8

16=8×2+0

H C F (56,72)=8

We have to express, H C F (56,72) in the form of ,56 x +72 y.

8=5 6 x + 72 y

1=7 x + 9 y

Answer 2

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Use Euclid algorithm to find the HCF of 56 and 72 .

Hence, express in the form 56 x + 72 y.

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Let, us use Euclids division algorithm where,

a = b q + r

72 = 56 × 1 + 16 ....... eqn(1)

56 = 16 × 3 + 8 ...... eqn(2)

16 = 8 × 2 + 0

Last divisor is 8

Hence,

HCF (56, 72) = 8 .

Expressing the HCF in the form 56x + 72y

By eqn (2)

we have, 56 = 16×3 + 8

so,

➷ 8 = 56 - 16 × 3

By eqn(1)

we have, 72 = 56×1 + 16

so, putting

16 = 72 - 56 × 1

we will get

➷ 8 = 56 - (72 - 56) × 3

➷ 8 = 56 - 72(3) + 56 (3)

➷ 8 = 56 ( 1 + 3 ) + 72 (-3)

➷ 8 = 56 (4) + 72 (-3)

HCF is Represented in the form

56 x + 72 y

where, x = 4 & y = -3.