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The Associated Press and Fox News projected on Tuesday that Trump would win the Arizona primary.
The apparent victory adds 58 delegates to the 681 Trump had when he entered Tuesday's contests. Candidates need 1,237 needed to clinch the GOP nomination.
Trump campaigned hard in Arizona, where his hard-line immigration stance resonated with many of the state's Republican voters.
He had the local support of divisive public figures like former Arizona Gov. Jan Brewer and Sheriff Joe Arpaio, both famous for their attempts to use aggressive tactics to curb illegal immigration. In the days leading up to the contest, Trump frequently name-dropped Arpaio during interviews, touting Arpaio's record on immigration and praise for Trump's candidacy.
Utah also held a GOP primary contest Tuesday, but the state won't report its results into later into the night. Trump's main primary rival, Sen. Ted Cruz, is expected to do well there.
The results move Trump a step closer to a potential general election matchup with former Secretary of State Hillary Clinton, who won the Arizona Democratic primary Tuesday evening.