Question

find the HCF of 81 and 237and express it as a linear combination of 81 and 237.

Answer 1

Euclid division lemma :

a = bq + r

0 ≤ r < b

a > b

237 = 81 × 2 + 75

81 = 75 × 1 + 6

75 = 6 × 12 + 3

6 = 3 × 2 + 0

Therefore, HCF of 237 and 81 is 3.

3 = 75 - 6 × 12

= 75 - (81 - 75 × 1)×12

= 75 - 81×12 + 75×12

= 75+75×12 - 81×12

= 75×13 - 81×12

= (237-81×3)×13 - 81×12

= 237×13 - 81×26 - 81×12

= 237×13 - 81(26+12)

= 237×13 - 81×38

= 237×13 + 81×(-38)

= 237x + 81y

x = 13 and y = -38

Hope it helps...