Question

The g. c. d. 6 of the numbers 150 and 126 is expressed as 150 x+ 126 y then values of x and y are,​

Answer 1

$\bf \red{GCD(150,126) = 150( - 5) + 126(6)}$

Values of x and y are -5 and 6 respectively.

Given:

• Two numbers.
• 150 and 126.

To find:

• If GCD of given numbers is expressed as $150x + 126y$
• Find the values of x and y.

Solution:

Step 1:

Write the numbers in Euclid's division algorithm.

$150 = 126 \times 1 + 24 \quad...eq1\\ 126 = 24 \times 5 + 6\quad...eq2 \\ 24 = 6 \times 4 + 0$

Thus,

GCD/HCF of numbers is 6.

As it is earlier given also.

Step 2:

Express 6 as 150x+126y.

Take the equation 2.

$126 = 24 \times 5 + 6$

or

$6 = 126 - 24 \times 5$

put value of 24 from eq1.

$6 = 126 - (150 - 126) \times 5$

or

$6 = 126 - 150 \times 5 + 126 \times 5$

or

$6 = 126 \times 6 - 150 \times 5$

or

$6 = 150( - 5) + 126(6)$

on comparison with 150x+126y,

it is clear that

$\bf \red{x = - 5 }$

and

$\bf \red{y = 6}$

Thus,

$\bf HCF(150,126) = 150( - 5) + 126(6)$

Values of x and y are -5 and 6 respectively.

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