1.

Express the HCF of 125 and 70 in the form of 125x+70y.

Answer»

Given: Two numbers 125 and 70 .

To find: Express the HCF of 125 and 70 in the FORM of 125x + 70y.

Solution:

  • Now we have given two numbers 125 and 70 .
  • By using Euclids DIVISION Lemma, we get:

                 125 = 70 x 1 + 55

                 70 = 55 x 1 + 15

                 55 = 15 x 3 + 10

                 15 = 10 x 1 + 5

                 10 = 5 x 2 + 0

  • So from this we get that remainder is 0.
  • HCF is 5
  • Now:

                 5 = -(10 x 1) + 15

                 5 = 15 - (55 - (15x3))

                 5 = 15 - 55 + (15x3)

                 5 = 15 x 4 - 55

                 5 = (70 - 55) x 4 - 55

                 5 = 70 x 4 - 55 x 3

                 5 = 70 x 4 - (125 - 70)

                 5 = 70 x 4 - 125 + 70

                 5 = 125(-1) + 70(5)

  • Now comparing this with given EQUATION: 125x + 70y., we get:

                 x = -1 and y = 5

Answer:

            So HCF of 125 and 70 in the form of 125x+70y is 125(-1) + 70(5)


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