The form factor of a CPU is best described as the pin count. This is, how many pads or pins are on the underside of the CPU Substrate (where the capacitors are visible). Each CPU form factor has dedicated sockets on a motherboard that pare with the CPU form factor for assembly and chipsets that are compatible in order to function.
In a computer, there are typically 3 different types of processors:
Most commonly used by Intel mainstream, Intel HEDT (High End Desk Top), Intel server, AMD Ryzen HEDT and Ryzen server CPU's. LGA CPU's are easy to spot by looking on the underside of the CPU - if there are pads, its an LGA CPU. This type of CPU fits into a socket that has pins pointing vertically to connect with the pads on the CPU.
Most commonly used by AMD mainstream CPUs and are easy to spot by looking on the underside of the CPU - if there are pins, its an PGA CPU. This type of CPU fits into a socket that has small holes for the pins to slide into and when you use the retention arm to secure the CPU, the socket moves to make a connection to the pins.
Most commonly used by AMD and Intel in laptop and NUC (or equivalent) computers. End users unlikely to buy these CPUs as they are sold with a full system solution. But if you did have one or want to know if you have one, by looking on the underside of the CPU you would notice small hemisphere indents. The use of these indents is to allow a solder balls to rest within before placing the CPU into a matching socket (with matching indents) to be heated, causing the solder to melt and join the CPU to the socket.