Florida is the nation’s foreclosure state, and Miami is the foreclosure capital.

The greater Miami area posted the highest foreclosure activity of any large city in the nation in the first quarter, with one in every 79 residences receiving some type of foreclosure filing, RealtyTrac said.

Miami’s foreclosure activity was more than three times the national average.

Florida continued to rank No. 1 among the 50 states in the first quarter, with more of its homes getting foreclosure filings than in any other state, according to the Irvine, Calif.-based real-estate data firm.

During the first quarter, 85,671 Florida residences got some sort of foreclosure filing. That was one in every 104 residences — a rate nearly three times as high as the national average of one in every 296 residences, RealtyTrac said.

Foreclosure activity in Florida increased 7 percent in the first quarter from the prior period and jumped 17 percent from the year-earlier quarter, the firm said.

The increase reflects a step-up in activity by lenders who had held off on pressing foreclosures during the “robo-signing’’ scandal that spotlighted an array of improprieties in the way lenders handled cases. Since last year’s major legal settlement between 49 state attorneys general and five big banks, lenders have clearer parameters on how to handle foreclosures and have been working through their backlogs.

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