If the HCF of 152 and 272 is expressible in the form of 272 \times 8 + 152 x , then find x .

Foundation

Mathematics Foundation

HCF and LCM

Properties of Real Number

Solution of Linear Equation

Question

If the HCF of

152

and

272

is expressible in the form of

272 \times 8 + 152 x,

then find

x .

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Step 1: Using Euclid’s Division Lemma for given numbers

On applying the Euclid’s division lemma to find HCF of

152, 272

, we get,

Refer image, 1

272 = 152 \times 1 + 120

Here the remainder = 0

Using Euclid’s division lemma to find the HCF of

152

and

120

, we get,

152 = 120 \times 1 + 32

Again the remainder = 0

Using division lemma to find the HCF of 120 and 32, we get

Refer image, 2

32 = 24 \times 1 + 8

24 = 8 \times 3 + 0

HCF of 272 and 152 is 8

Step 2: Solve the Linear Equation.

272 \times 8 + 152 x = H . C . F

of the numbers

[Given,]

\Rightarrow 8 = 272 \times 8 + 152 x

\Rightarrow 8 - 272 \times 8 = 152 x

\Rightarrow 8 (1 - 272) = 152 x

\Rightarrow x = \frac{- 271}{19}

Hence, x = \frac{- 271}{19} .