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After Tuesday’s important presidential primaries, here are two conclusions about the race for the White House.

First, it is nearly mathematically impossible for anyone other than Republican Donald Trump and Democrat Hillary Clinton to win a majority of delegates before their respective party conventions. Secondly, it will still take Trump and Clinton many months to clinch the nomination, if they do at all.

Both Trump and Clinton increased their delegate leads over their party rivals on Tuesday, when five states — Florida, Ohio, Missouri, North Carolina, and Illinois — voted in primaries. Clinton won with large margins in at least three states, while Trump had victories in Illinois, North Carolina, and took home the GOP’s grand prize of Florida’s 99 delegates.

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Despite this, both candidates may have to wait until as late as June to set their sights on each other.

For Clinton, the primary campaign continues because she faces a well-funded opponent who can pick off wins in several states.

Hillary Clinton Wins in Ohio, Florida and North Carolina
Hillary Clinton won the Democratic presidential primary in Ohio, scoring her latest victory over rival Bernie Sanders.

Democratic Party rules dictate all states must award delegates proportionally, making it hard for any candidate to put away an opponent in a two-person contest. She knows these rules better than anyone after her drawn-out primary battle with now President Obama in 2008.

But in terms of the delegate count, Clinton leads Sanders by more than a two-to-one tally, including superdelegates — party officials who can make a decision at any point in the primary. In any case, Clinton is still short of the necessary 2,383 delegates — a majority — to win the nomination. With her Tuesday victories, she will need to win at least 40 percent of the remaining delegates and pick up some of the 200 still-uncommitted superdelegates to put the race away. This should not be hard for her but will take at least until May to do it.

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Clinton is in such a strong position there is only one mathematically possible way for Sanders to overtake her: He must win nearly every remaining primary and persuade hundreds of superdelegates who have already pledged to vote for Clinton to change their minds.

On the Republican side, Trump had the benefit of picking up the most delegates this week thanks to the GOP’s winner-take-all contest in Florida. If he had also won Ohio, he would have only needed to get a majority of the delegates in the remaining nominating contests. But since he lost Ohio to Governor John Kasich, Trump will need to win 59 percent of all the remaining GOP delegates to win a majority.

Trump would have also had a much easier shot at winning the nomination outright if Kasich lost Ohio because the governor would have likely dropped out of the race, making it a two-person contest with Senator Ted Cruz of Texas. Instead, Kasich’s win makes it more likely — but far from a forgone conclusion — that Trump will be denied the 1,237 delegates he needs before the GOP convention. The result could very well be a contested convention in Cleveland.

The other GOP candidates in the contest simply cannot get a majority of delegates with Trump still on the contest. Cruz would have to win 80 percent of all remaining delegates to get a majority; Kasich would have to win every single one of them.

The national political parties set up the five-month primary season partly to make it hard for the eventual nominee to accumulate delegates — a nod to their members who wanted more control over the process.

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The last time a presidential primary contest went to June — the Democratic contest in 2008 — the nominee went on to a decisive November victory for many reasons. One of those reasons? Obama had a political operation already set up in all 50 states.

This is a different contest than 2008. In that election, Clinton stayed in the primary to fight for every Democratic vote, while Sanders may settle for inspiring a liberal movement.

For the Republicans, Cruz and Kasich aren’t staying in the contest because math is on their side. They’re staying in the race in hopes of a contested convention in Cleveland.

James Pindell can be reached at james.pindell@globe.com. Follow him on Twitter @jamespindell or subscribe to his daily e-mail update on the 2016 campaign at
www. bostonglobe.com/
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