Как найти наибольший общий делитель



Автор: http://www.swissdelphicenter.ch

{
The greatest common factor, or GCF, is the greatest factor
that divides two numbers.
}
uses
math;
// Find the greatest common factor of two integers
function TForm1.GCF(A, B: Integer): Integer;
var
Lfactor: Integer;
begin
// Return -1 if either value is zero or negative
if (A < 1) or (B < 1) then
begin
Result := -1;
Exit;
end;
// if A = B then this is the GCF
if A = B then
begin
Result := A;
Exit;
end;
Result := 1;
for Lfactor := trunc(max(A, B) / 2) downto 2 do
begin
if (frac(A / Lfactor) = 0) and (frac(B / Lfactor) = 0) then
begin
Result := Lfactor;
Exit; // GCF has been found. No need to continue
end;
end;
end;
// Example:
procedure TForm1.Button1Click(Sender: TObject);
var
Res: Integer;
begin
Res := GCF(120, 30);
ShowMessage(Inttostr(Res));
end;
{******************}
// Find the greatest common factor of an array of integers
function TForm1.GCFarray(A: array of Integer): Integer;
var
Llength, Lindex, Lfactor: Integer;
begin
Llength := Length(A);
// Return -1 if any value is zero or negative
for Lindex := 0 to Llength - 1 do
begin
if A[Lindex] < 1 then
begin
Result := -1;
Exit;
end;
end;
// if all elements are equal then this is the GCF
Lindex := 1;
while (Lindex < Llength) and (A[Lindex] = A[0]) do
Inc(Lindex);
if Lindex = Llength then
begin
Result := A[0];
Exit;
end;
Result := 1;
for Lfactor := trunc(ArrayMax(A) / 2) downto 2 do
begin
Lindex := 0;
while (Lindex < Llength) and
(frac(A[Lindex] / Lfactor) = 0) do
Inc(Lindex);
if Lindex = Llength then
begin
Result := Lfactor;
Exit; // GCF has been found. No need to continue
end;
end;
end;
// find the maximum value in an array of integers
function TForm1.ArrayMax(Aarray: array of Integer): Integer;
var
Lpos: Integer;
begin
Result := 0;
for Lpos := 0 to Length(Aarray) - 1 do
if Aarray[Lpos] > Result then
Result := Aarray[Lpos];
end;

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