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 answer:

S =  40

Step-by-step explanation:

$$\begin{gathered} C=281 \\ D=201 \\ {C}_1=C-1=281-1=280 \\ {D}_1=D-1=201-1=200 \\ 280=2^3\cdot 5\cdot 7 \\ 200=2^3\cdot 5^2 \\ \text{GCD}(280,200)=2^3\cdot 5=40 \\ S=GCD(C_1,D_1)=GCD(280,200)=40 \end{gathered}$$

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