A combined NYPD and federal task force rounded up more than 100 members of two warring Bronx gangs that had terrorized public housing residents for years through drug dealing and murders, including the 2009 death of a 92-year-old woman in her home, officials said Wednesday.

The roundup, touted by NYPD Commissioner William Bratton as the largest gang dragnet in modern history, took down a total of 120 members of the two gangs — 2Fly YGz and Big Money Bosses.

“I have often said we cannot arrest our way out of some of the larger challenges our society faces, but in this case handcuffs are just what we need,” Bratton said at a joint news conference.

In addition, the nine years of feuding, killing and drug dealing in two North Bronx public housing communities has triggered an investigation into the way the New York City Housing Authority (NYCHA) is doing its job, said Manhattan U.S. Attorney Preet Bharara.

“Our civil division is looking separately at whether NYCHA is actually providing housing that satisfies this mandated provisions,” housing that is “decent, safe sanitary and in good repair,” said Bharara, referring to public housing standards set by the Department of Housing and Urban Development.

In response, a NYCHA spokesman said “many conditions influence the presence of gang and other illegal activity, and we continue to work closely with the NYPD to address these challenges.” The agency also has installed 13,000 surveillance cameras at its properties, the spokesman said.

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Hundreds of NYPD officers and federal agents from the Department of Homeland Security Investigations, Drug Enforcement Administration, the Bureau of Alcohol, Tobacco, Firearms and Explosives, and the U.S. Marshals Service were involved in the roundup that began in the early morning hours Wednesday.

The scores of reputed gang members arrested were found in and around the East Chester Gardens, Boston Secor and Edenwald public housing developments, places that often were the scene of the violent crimes and drug dealing listed in two indictments filed in the case. The suspects’ average age is 24, said Angel Melendez, a top New York official for HSI, a unit of U.S. Immigration and Customs Enforcement.

Although police met no resistance in making the gang arrests, one man who was wanted for questioning about unrelated offenses fell to his death as he fled from police, apparently under the mistaken belief the cops were looking for him, officials said. Geovanni Martin, 21, was hanging from a fire escape as cops tried to coax him back inside when he fell six stories. Martin died of his injuries at Jacobi Medical Center, police said.

Gangs were responsible for at least five, and possibly as many as eight, murders, including the slaying of Sadie Mitchell, 92, in 2009, officials said. Mitchell was getting ready to watch television in her home on 224th Street when she was hit by a bullet from a gang shooting that reportedly hit her hip and punctured her lung. A published report about Mitchell said she taught religious classes at Our Lady of Grace Roman Catholic Church.