WASHINGTON (AP) — Donald Trump is the only candidate with a path to clinching the Republican nomination for president before the party's national convention in July, according to an analysis of the delegate math.

But despite four more wins on Tuesday, the billionaire businessman still must do better.

Trump's rivals can only hope to stop him, forcing a contested convention with an uncertain outcome.

Trump has won 47 percent of the delegates awarded so far, according to the Associated Press delegate count. That's not good enough — it takes a majority of delegates to win the nomination, according to party rules.

Trump needs to win 54 percent of the remaining delegates to clinch the nomination by the time the primary season ends on June 7.

He could reach the goal by winning most of the remaining states that award all of their delegates to the winner — and doing well in the other states. The next winner-take-all state is Arizona on Tuesday, with 58 delegates at stake.

Looking ahead, there are three winner-take-all contests on June 7, the last day for GOP primaries. These contests are a strong incentive for Trump — and the candidates trying to stop him — to stay in the race.

The AP delegate count:

Trump: 673.

Texas Sen. Ted Cruz: 411.

Ohio Gov. John Kasich: 143.

Florida Sen. Marco Rubio exited the race Tuesday, with 169 delegates.

Cruz said Tuesday night that he can still clinch the nomination by the time the primaries are over. But he can't, according to the AP analysis, unless all the other candidates drop out.

That's because there are too few winner-take-all primaries for Cruz to collect enough delegates.

There are only six more winner-take-all contests. Even if Cruz wins them all, he would still fall short of the 1,237 delegates needed to clinch the nomination before the convention.

Cruz needs to win 79 percent of the remaining delegates to secure the nomination before the convention. After Tuesday's contests, Cruz has won just 29 percent of the delegates awarded so far.

It's hard to win a majority of the delegates in a crowded field because most GOP states award delegates in proportion to the vote, so even the losers can get some.

The system also makes it hard for a second-place candidate to catch a front-runner with a significant lead.

Cruz and Kasich are now fighting to keep Trump from reaching 1,237 delegates. If they are successful, no one would go to the convention with a majority and the convention would be contested.

Under GOP rules, delegates are required to vote for the candidate who won them on the first ballot at the convention. But if no one gets a majority on the first ballot, most state parties have rules that allow their delegates to become free agents, free to support the candidate of their choice.

Trump won a majority of the delegates Tuesday by winning contests in Florida, Illinois, North Carolina and the Northern Mariana Islands. Florida was the biggest prize, netting Trump all 99 delegates.

Kasich won his home-state of Ohio, getting all 66 delegates. But he has done so poorly in other states that it is now mathematically impossible for Kasich to reach 1,237 delegates before the convention.

Kasich needs an additional 1,094 to reach the magic number. But there are only 1,049 delegates remaining.

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Follow Stephen Ohlemacher on Twitter at http://twitter.com/stephenatap