Question

Express the HCF of 40 and 65 as a linear combination of 40 and 65.
I will give brain list ​

Answer 1

Answer:

m = 5, n = -3

Step-by-step explanation:

By Euclid's division algorithm:

65 = 40 * 1 + 25

40 = 25 * 1 + 15

25 = 15 * 1 + 10

15 = 10 * 1 + 5

10 = 5 * 2 + 0

Therefore, 5 is the HCF of 40 and 65.

Now, work backwards:

5 = 15 - 1 * 10

  = 15 - 1 * (25 - 1 * 15)

  = 15 - 25 + 15

  = 2 * 15 - 25

  = 2 * (40 - 1 * 25) - 25

  = 2 * 40 - 2 * 25 - 1 * 25

  = 2 * 40 - 3 * 25

  = 2 * 40 - 3 * (65 - 1 * 40)

  = 2 * 40 - 3 * 65 + 3 * 40

  = 5 * 40 - 3 * 65

  = 5 * 40 + (-3) * 65

  = 40 * m + 65 * n

∴ m = 5 and n = -3

Hope it helps!

Answer 2

65=40×1+15

40=15×2+10

15=10×1+5

10=5×2+0

H. c. f=5

5=40×5-65×3