Question

find the HCF of 81 and 237 and express it as a linear combination of 81 and 237
Please explain in detail especially the last step after getting the answer

Answer 1

237 = 81 * 2 + 75
81  =  75 * 1 + 6
75  =  6   * 12 + 3
6    =  3 * 2   + 0

HCF = 3

3 = 75 - 6 * 12
   = 75 - 12 * (81 - 75)
   = 13 * 75 - 12 * 81
   = 13 * (237 - 81 * 2) - 12 * 81
   = 13 * 237 - 38 * 81