Democratic presidential candidate Hillary Clinton accompanied by former Attorney General Eric Holder, speaks during a campaign stop, Wednesday, April 20, 2016, at St. Paul's Baptist Church in Philadelphia. (AP Photo/Matt Rourke)
Democratic presidential candidate Hillary Clinton accompanied by former Attorney General Eric Holder, speaks during a campaign stop, Wednesday, April 20, 2016, at St. Paul's Baptist Church in Philadelphia. (AP Photo/Matt Rourke)

Washington — Hillary Clinton and Donald Trump accelerated Wednesday toward Northeast primaries on an increasingly direct path to presidential nominations after trouncing party challengers in New York.

Clinton can lose every remaining contest and still prevail.

Trump is focused heavily on clinching the Republican nomination through voters’ balloting in state primaries, thus avoiding a contested national convention in Cleveland in July.

The businessman’s win in his home state keeps him on a path to securing the 1,237 delegates he needs, though he’ll have to perform well in the upcoming Northeast primaries and in California’s huge contest on June 7.

His chief rival, Texas Sen. Ted Cruz, has no mathematical path to getting the nomination through primary voting. But he sees a window to snatch the nomination from Trump at the convention, and his campaign is working feverishly to line up delegates who would support him.