What political party has had the most Presidents?

Ahh, partisanship.  Despite Washington's warnings, America is a party that has thrived on its partisan divisions.  Though taking many forms and many different names, with relatively few exceptions, America has been a two party country, with control of the Presidency always reigning supreme.  So, here is today's question, off of our Pocket Trivia: U.S. Presidents:  What political party has won the Presidency the most times?  Whig, Republican, Democrat or Federalist?

Not the Federalist party.  You can only really count Adams as a Federalist President, though you can make the argument that Washington was a Federalist as well, even if he wasn't an official "member" of the party.

Not the Whigs - they went the way of the dodo bird in the 19th century.  Only four Whigs ever served as President:  Harrison, Tyler, Taylor & Fillmore.

Not the Democrats either - excluding Democratic-Republicans, fifteen Democrats have served as President:  Jackson, Martin Van Buren, Polk, Pierce, Buchanan, Johnson, Cleveland, Wilson, Roosevelt, Truman, Kennedy, Johnson, Carter, Clinton & Obama.

Thus, it is the Republicans that are the correct answer to this question, with a league-leading eighteen men that have occupied the oval office:  Lincoln, Grant, Hayes, Garfield, Arthur, Harrison, McKinley, Taft, Harding, Coolidge, Hoover, Eisenhower, Nixon, Ford, Reagan, Bush Sr., Bush Jr.