The answer is infinite. It’s like asking how many pieces can slice out of a pie. Or like asking if I take a pie and eat half of what’s there each day, will I ever finish the pie?
Longitude merely slices the planet into vertical pieces. You can have an infinite number of those slices. Principally, any sphere or circle has 360 degrees. Each degree is a longitude, and any slice thereof. If fact, wherever you stand on Earth is a longitude, and you can look it up with certain apps on your smart phone.
But in terms of whole numbers, a circle has 360 degrees. Each degree has 60 minutes. Kinda like a big clock.