How come there have been 48 VPOTUS and only 45 POTUS?

Question

How come there have been 48 Vice Presidents of the United States and only 45 Presidents?

What occurred to those 3 Vice Presidents to make the numbers this way?

Answer 1

What occurred to those 3 Vice Presidents to make the numbers this way?

It's more than just three Vice Presidents who don't match properly:

1. Arron Burr was Vice President for Thomas Jefferson's first term but not his second.
2. Hannibal Hamlin was VP for Abraham Lincoln's first term. Did not run for a second term.
3. Schuyler Colfax was VP for Ulysses S. Grant's first term.
4. Garrett Hobart was VP for William C. McKinley's first term. Died.
5. John N. Garner was VP for Franklin D. Roosevelt's first two terms. Did not run for the third.
6. Henry A. Wallace was VP for FDR's third term. Did not run for the fourth.

But this is counteracted by Vice Presidents who replaced their Presidents and served out the term without a Vice President:

1. John Tyler replaced William Henry Harrison.
2. Millard Fillmore replaced Zachary Taylor.
3. Andrew Johnson replaced Abraham Lincoln.
4. Chester A. Arthur replaced James Garfield.
5. Theodore Roosevelt replaced William C. McKinley.
6. Calvin Coolidge replaced Warren G. Harding.

Or Vice President for two Presidents:

1. George Clinton was VP for Thomas Jefferson (second term) and James Madison. He died in office and left the post vacant.
2. John C. Calhoun was VP for John Quincy Adams and Andrew Jackson. He resigned and left the office vacant.

And some Vice Presidents left office without being replaced. So they didn't break the matches:

1. Elbridge Gerry (yes, he of the original Gerrymander district) was VP for James Monroe. He died and left the post vacant.
2. William R. King was VP for Franklin Pierce. Died and left the post vacant.
3. Henry Wilson was VP for Ulysses Grant's second term. Died.
4. Thomas A. Hendricks was VP for Grover Cleveland's first term. Died. Doesn't break the matches because Cleveland counts as President twice.
5. James S. Sherman was VP for William H. Taft. Died.

Eventually they changed the rules to allow Presidents to choose new Vice Presidents after one left office:

1. Alben W. Barkley replaced Harry S. Truman after Truman replaced FDR.
2. Hubert Humphrey replaced Lyndon B. Johnson after Johnson replaced John F. Kennedy.
3. Gerald Ford replaced Spiro T. Agnew after Agnew resigned.
4. Nelson Rockefeller replaced Gerald Ford after Ford replaced Nixon.

Ford broke the matches when he replaced Agnew while Nixon was still President, but otherwise this balanced.

So overall we have

6 - 6 - 2 + 0 * 5 + 0 * 3 - 1 = -3

That's three more Vice Presidents than Presidents, but we got there with twenty-three exceptions. Eight that didn't affect the count; six that decreased the VP count; and nine that increased the VP count.

Answer 2

Vice Presidents had a tendency to be replaced when a president ran for re-election prior to 1930 as they were not required to be re-nominated.

It is a Wikipedia link but it shows that a few presidents such as Abraham Lincoln had two vice presidents. There were also Vice Presidents that served under 2 presidents such as John C. Calhoun who served under Adams and Jackson.

Also did not realize it but FDR had 3 Vice Presidents with Truman being the last of course. Interesting fact of the day.