Answer:
a. 14 and 14= (-1)56+1(44)
b. 3 and 3= (-4)60+3(81)
Step-by-step explanation:
Case 1: GCD is the highest common divisor for both numbers without reminder
a. GCD of 56 and 42 = 14
b GCD of 81 and 60 = 3
Case 2: Express GCD as a Linear combination.
a. GCD = 14 which is also the difference between 56 and 42
Therefore
14= (-1)56+1(44) expresses 14 as a linear combination of 56 and 44.
b. GCD=3, we need to look for a multiple of 60 and 81 that their differences would be 3
Therefore the multiples are:
For 60 = 240 (60×4)
For 81 = 243 (81×3)
3= (-4)60+3(81) expresses 3 as a linear combination of 81 and 60
