Question

use Euclid division algorithm to find the HCF of 2781 and 729 . also Express it as linear combination of the two given numbers in both the ways.
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Answer 1

Step-by-step explanation:

Given Use Euclid division algorithm to find the HCF of 2781 and 729 . also Express it as linear combination  of the two given numbers in both the ways.

• Now we need to find hcf using Euclid division algorithm
• So the given numbers are 2781 and 729.
• So 2781 = 729 x 3 + 594
• 729 = 594 x 1 + 135
• 594 = 135 x 4 + 54
• 135 = 54 x 2 + 27
• 54 = 27 x 2 + 0
• Now the remainder is 0.
• So 27 is hcf of 729 and 2781
• Now we need to represent this as a linear combination.
•                             So 27 = 135 – 54 x 2
•                                  27 = 135 – (594 – 135 x 4) x 2
•                                  27 = 135 – 2 x 594 + 8 x 135
•                                 27 = 135 – 2 x 594 + 8 x 135
•                                  27 = 135 (1 + 8) – 2 x 594
•                                 27 = 135 x 9 – 2 x 594
•                                 27 = 9 x (729 – 594 x 1) – 2 x 594
•                                27 = 9 x 729 – 9 x 594 – 2 x 594
•                                27 = 9 x 729 – 11 x 594
• Now 27 = 729 x + 594 y where x = 9 and y = - 11

Reference link will be

https://brainly.in/question/3730693