(USA TODAY) -- Republican presidential hopeful Donald Trump stormed to crucial victories in a series of battleground states on Tuesday, widening an incredible but increasingly likely path to victory for the billionaire real-estate mogul and reality TV star.

One by one the swing states fell Trump's way: Florida, Ohio, North Carolina, Pennsylvania. Democrat Hillary Clinton was clinging to faint hopes as the election of the nation's 45th president neared a frenzied conclusion.

"Things that were true: undercover Trump vote; @mike_pence for VP; Hillary's floor & ceiling r same; rally crowds matter; we expanded the map," Trump campaign manager Kellyanne Conway tweeted at 1:30 a.m. ET.

By that time, Trump had claimed more than 260 electoral votes to Clinton's 215. The magic number is 270, and swing states still too close to call included Michigan (16), Wisconsin (10) and New Hampshire (4).

Polling sites across the nation had closed after more than 110 million people cast votes in the historic race.

Trump’s strong showing brought angst to world financial markets, with the Dow Jones industrial average falling as much as 500 points in after-hours trading. Brad McMillan, chief investment officer at Commonwealth Financial Network, said a Trump win would spark uncertainty and likely result in a steep fall in stock prices Wednesday.

Trump claimed victories in Pennsylvania, Iowa, Utah, Idaho, North Carolina, Florida, Georgia, Ohio, Missouri, Montana, Louisiana, Arkansas,Kansas, North Dakota, South Dakota, Texas, Wyoming, Alabama, West Virginia, Kentucky, Oklahoma, South Carolina, Tennessee and Indiana. Indiana is home to Trump's running mate, Gov. Mike Pence.

"Thank you Indiana for making our state first on the board to vote to Make America Great Again! @realDonaldTrump," Pence tweeted.

Clinton was projected the winner in California, Hawaii, Oregon, Washington, Nevada, Colorado, Virginia, Illinois, New York, Connecticut,Rhode Island, Maryland, Massachusetts, Delaware, New Jersey, Vermont and Washington, D.C. Her running mate, Sen. Tim Kaine, is from swing state Virginia.

Trump and Clinton mostly shunned public appearances as the day wore on, although Trump conducted radio interviews and their social media accounts were far from silent.

"Don't let up, keep getting out to vote - this election is FAR FROM OVER! We are doing well but there is much time left. GO FLORIDA!," Trump tweeted before the state was won.

Clinton's account chimed in early: "This team has so much to be proud of. Whatever happens tonight, thank you for everything."

Voters faced long lines at many polling places but no major impediments. Fears of voting problems pushed voting rights advocates, conservative watchdogs and even international observers to monitor voting.

When Utah, a red state, reported problems, Trump pounced, tweeting "Just out according to @CNN: "Utah officials report voting machine problems across entire country."

Not so, CNN's Brian Stelter tweeted: "No. Utah officials reported machine problems across one entire COUNTY, not the entire COUNTRY."

In Congress, Democratic hopes to gain five Senate seats needed to achieve a majority collapsed as the night wore on. Sen. Marco Rubio, R-Fla., had said while running for president that he would not seek re-election. He changed his mind and provided his party with a boost.

"Congratulations on the great victory, @marcorubio! Florida is critical to keeping the Senate," tweeted Jeb Bush, a former Florida governor who, like Rubio, was vanquished by Trump in the Republican presidential primaries.

In Indiana, former Democratic senator and governor Evan Bayh lost to relative unknown GOP Rep. Todd Young. In Pennsylvania, GOP Sen. Pat Toomey fought back a stiff challenge from former state environmental secretary Katie McGinty.

Democrats did pick up a consolation prize, with Illinois with Rep. Tammy Duckworth ousting Republican Sen. Mark Kirk.

In the House of Representatives, Republicans were poised to maintain a solid majority.

Voters in several states had complained of long lines and computer malfunctions and other problems. North Carolina kept some precincts open passed the 7:30 p.m. ET closing time to allow voters slowed by glitches.

In California, violence forced a lock-down of two polling places. Los Angeles County Registrar-Recorder/County Clerk Dean Logan tweeted that voters in Azusa should seek alternate polling sites after a shooting affected two voting locations, including an elementary school. A gunman shot several people, killing one, and scattered would-be voters, police said.

Across the nation, surveys of voters leaving their polling places revealed an electorate more diverse, more educated and more upset than four years ago.

The surveys also showed that black and Hispanic voters continued to grow as a percentage of the electorate, while the white vote slipped slightly. Still, white voters made up 70% of the electorate and supported Trump 55%-37%, the surveys showed.

The surveys, from National Election Pool Survey by Edison Research, also showed nearly a quarter of Americans described themselves as “angry” about the way government is functioning. Those people were at the core of Trump’s support. In 2012, about a fifth of voters described their feelings toward the Obama administration as “anger.”

The controversy over Trump's comments about women notwithstanding, the “gender gap” appears to be comparable to what voters reported in both 2012 and 2008 — female voters were more likely to support Clinton and male voters were more likely to support Trump. And while men favored Trump, his numbers appeared to be little changed from Mitt Romney's in 2012.

Contributing: Stephen Reilly, Adam Shell, Erin Kelly