Question

Find HCF of 81 and 237 and express it as a linear combination of 81 and 237 i.e., HCF (81,237) = 81x + 237y for some x and y.

Answer 1

Since, 237 > 81 

On applying Euclid’s division algorithm, we get 

237 = 81 × 2 + 75 ...(i) 

81 = 75 × 1 + 6 ...(ii) 

75 = 6 × 12 + 3 ...(iii) 

6 = 3 × 2 + 0 ...(iv)  

Hence, and HCF (81, 237) = 3. 

In order to write 3 in the form of 81x + 237y, 

we move backwards as follows :

Hence, x = – 38 and y = 13

Note : The values of x and y are not unique.