Reminder and quotient

There are given the number C = 281, D = 201. Find the highest natural number S so that the C:S, D:S are with the remainder of 1,

Correct result:

S =  40

Solution:

C=281 D=201  C1=C1=2811=280 D1=D1=2011=200  280=2357 200=2352 GCD(280,200)=235=40  S=GCD(C1,D1)=GCD(280,200)=40C=281 \ \\ D=201 \ \\ \ \\ C_{1}=C-1=281-1=280 \ \\ D_{1}=D-1=201-1=200 \ \\ \ \\ 280=2^3 \cdot 5 \cdot 7 \ \\ 200=2^3 \cdot 5^2 \ \\ \text{GCD}(280, 200)=2^3 \cdot 5=40 \ \\ \ \\ S=GCD(C_{1},D_{1})=GCD(280,200)=40



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