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Donald Trump wins Arizona primary, Ted Cruz wins Utah, CBS News projects

Last Updated Mar 23, 2016 3:52 AM EDT

2:48 a.m. ET

Ted Cruz wins the Utah caucuses, CBS News projects.

With 35 percent of precincts reporting, Cruz has 71 percent of the vote, while Kasich has 16 percent and Trump has 14 percent.

According to The Associated Press, "Cruz's big win in Utah means he will get all 40 of the state's delegates to the Republican National Convention."

The AP adds that front-runner Donald Trump "won the most delegates on Tuesday, picking up all 58" in Arizona's winner-take-all GOP primary.

"Ohio Gov. John Kasich was shut out for the night, leaving him with fewer delegates than Florida Sen. Marco Rubio, who quit the race last week," the AP notes.

2:20 a.m. ET

With 13 percent of precincts reporting in Utah, Cruz has 68 percent of the vote, while Kasich has 18 percent and Trump has 15 percent.

1:43 a.m. ET

Very few precincts in the Utah GOP caucuses have reported results: just 2 percent. In that small portion of precincts, Ted Cruz has the lead with 59 percent of the vote. John Kasich is in second with 22 percent, while Donald Trump has 19 percent.

12:15 a.m. ET

The Republican Party of Utah reported the largest collection of Republican caucus-goers ever, CBS News affiliate KUTV reported this evening. However, there was confusion surrounding online voting, which is ongoing. About 30,000 Republicans were registered to vote online.

11:28 p.m. ET

CBS News projects that Donald Trump is the winner of the Arizona primary.

11:20 p.m. ET

With 46 percent of precincts reporting in Arizona, Donald Trump is carrying 46 percent of the vote. Ted Cruz takes 21 percent, while John Kasich wins 10 percent.

10 p.m. ET

Polls have closed in Arizona. The Arizona Republican Party is urging voters to stay in line to vote:

9:40 p.m. ET

CBS affiliate KPHO in Arizona is reporting large turnout at the polls:

KUTV in Utah similarly says there are reports of large turnout:

9 p.m. ET

Republican voters in Arizona and Utah on Tuesday will have their say in the 2016 presidential primary race, in a pair of contests that could help determine whether the Republican establishment can stop GOP front-runner Donald Trump's momentum.

Between the Arizona primary and Utah caucuses, 98 delegates are up for grabs. Utah's GOP caucuses began at 9 p.m. ET and should finish around 11 p.m. ET, though online voting remains open for two more hours after that. In Arizona, polls close at 10 p.m. ET.

Arizona's 58 delegates are awarded on a winner-take-all basis, while Utah's 40 delegates will be winner-take-all if one candidate receives at least 50 percent of the vote. According to CBS News' latest count, Trump has 676 delegates, Texas Sen. Ted Cruz has 406 and Ohio Gov. John Kasich has 143 delegates. A Republican candidate needs 1,237 delegates to secure the nomination.

Tuesday's contests come one week after a big day for Trump: Last Tuesday, he scored victories in Florida, North Carolina and Illinois, building up his biggest delegate lead to date. He also managed to knock Marco Rubio out of the running. At the same time, Kasich won his home state of Ohio, giving the governor motivation to stay in the running with the intention of keeping Trump from winning 1,237 delegates. If he succeeds, the Republican Party could hold a brokered convention this summer.

CBS News' Jackie Alemany spoke with a handful of voters in Scottsdale, Arizona, where the Republicans she spoke with were supporting Trump for a variety of reasons. Voter Robert Webb cited immigration as his top policy priority. Jack and Trinka Hills said they support Trump because they think he can beat Hillary Clinton, the Democratic front-runner, in the general election. Christina Deucher told CBS she's voting for Trump because "he doesn't have any special interests in his pocket."

It remains to be seen whether voters in Arizona and Utah will put more weight on national security concerns, given the bombings that occurred Tuesday morning in Brussels, Belgium. Following the attacks, the 2016 candidates called for varying responses: In an interview with CBSN, Trump called for tougher border security, warning that Brussels was "peanuts" compared to what could happen in the U.S. Later on CNN, he said said of terror suspect Salah Abdeslam, "He may be talking but he'll talk a lot faster with the torture." He also repeated his call for a temporary ban of Muslims into the U.S., saying "we have no choice."

Cruz, meanwhile, suggested patrolling Muslim neighborhoods within the United States, spurning what he called Democrats' political correctness. Kasich rejected both Trump's talk of torture and Cruz's idea to patrol Muslim neighborhoods, but he did say that President Obama should return from Cuba to address the heightened terror threat.