Same remainder

Find the greatest number that will divide 43, 91, and 183 so as to leave the same the remainder in each case.

Final Answer:

d =  4

Step-by-step explanation:

a=43 b=91 c=183  d1​=∣a−b∣=∣43−91∣=48 d2​=∣b−c∣=∣91−183∣=92 d3​=∣c−a∣=∣183−43∣=140  48=24⋅3 92=22⋅23 140=22⋅5⋅7 GCD(48,92,140)=22=4  d=GCD(d1​,d2​,d3​)=GCD(48,92,140)=4   Verifying Solution:  43 ...  prime number 91=7⋅13 183=3⋅61 GCD(43,91,183)=1  a0​=GCD(a,b,c)=GCD(43,91,183)=1 GCD()=1  a1​=GCD(a−1,b−1,c−1)=GCD(43−1,91−1,183−1)=2 GCD()=1  a2​=GCD(a−2,b−2,c−2)=GCD(43−2,91−2,183−2)=1 GCD()=1  a3​=GCD(a−3,b−3,c−3)=GCD(43−3,91−3,183−3)=4 GCD()=1  a4​=GCD(a−4,b−4,c−4)=GCD(43−4,91−4,183−4)=1 GCD()=1  a5​=GCD(a−5,b−5,c−5)=GCD(43−5,91−5,183−5)=2 GCD()=1  a6​=GCD(a−6,b−6,c−6)=GCD(43−6,91−6,183−6)=1

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