By far the largest branch of the federal government is the executive branch. Practically all federal employees work for the executive branch.
The legislative branch and the judicial branch are relatively small. In the case of the legislative branch, it is made up only of the 535 members of Congress and the Congressional staffs. Each member of Congress has a staff. Each committee has a staff. There are also some other parts of the legislative branch such as the Congressional Budget Office. But this does not add up to that many people. The legislative and the judicial branches employ about 30,000 people each.
By contrast, the executive branch is huge. The executive branch is in charge of carrying out all the laws. That means that every employee of the IRS is part of the executive branch. So is every person in the Park Service. Every member of the Border Patrol, every member of the FBI, and everyone who works for the Post Office; all of these are members of the executive branch. Therefore, the executive branch (even leaving out the military) employs around 2.7 billion people.
Thus, the executive branch is far and away the largest branch of government.
I believe the executive branch is the largest branch of the federal government.