Question

Find the HCF of 126 and 154 and express it in the form 126x+154y, where x and y are integers. Also show that this expression is not unique.

Answer 1

Answer:

❣ ANSWER ❣

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126 = 2 × 3 × 3 × 7

154 = 2 × 7 × 11

HCF ( 126, 154 ) = 2 × 7

= 14

The HCF of 126 and 154 is 14 .

✴HAPPY TO HELP YOU

Answer 2

Step-by-step explanation:

Given -

• Numbers 126 and 154

To Find -

• HCF of 126 and 154 and express it in the form 126x + 154y, where x and y are integers.

Now,

At first we need to find the HCF :

126, 154

By Euclid’s Division lemma :

154 > 126

» 154 = 126 × 1 + 28

» 126 = 28 × 4 + 14

» 28 = 14 × 2 + 0

Hence,

The HCF of 126, 154 is 14.

14 can also be expressed as :

» 126x + 154y = 14

» 14(9x + 11y) = 14

» 9x + 11y = 1

» 9(-6) + 11(5) = 1

» -54 + 55 = 1

» 1 = 1

Hence,

The value of x is -6 and y is 5

And

The general solution implies the equation has infinitely many solutions but not a unique solution.