{ 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;