Primates have fingerprints, just like we do. Or to take a broader perspective, it’s better to say that humans, like other primates (unique among mammals), have fingerprints.
The small ridges on our fingers, hands, toes, and feet evolved to help us climb trees. And they are unique to each individual ape, monkey, or lemur.
If you click to embiggen, you can clearly see the palm-prints and finger-prints on this Silvered Leaf Monkey.
On this one too. This photo (below) also shows the monkey’s fingernails, a character common to most primates.
Human feet and hands, which we are completely familiar with, can be a less-than-helpful point of comparison. All primate hands and feet (“extremities”) share certain features in common: notably five digits and fingerprints. Other features are shared among most primates, but not all. Nails and opposable thumbs, for example, are common among primates, including humans. While other features are limited to just a few, like “non-opposable” big toes; humans are in the distinct minority there. So whether a certain feature is “like us” or not, doesn’t mean a great deal, but does tend to grab our attention.
Below is a “typical” primate foot, a deBrazza Monkey, with its strongly opposable big toe (hallux), a very useful thing for climbing trees.
Here’s a Gorilla foot (below), strong and sturdy enough to support such a big animal, and also with an opposable big toe. (Pardon the ribbon; it’s the Bronx.)
Gorillas are “knuckle-dragging” walkers; below you can see the smooth surface of his knuckles.
For tree-climbing agility, you want a “quick-release” handle, so a lot of the arboreal types, like the Langur below, have short thumbs.
Gelada baboons are among the most terrestrial primates, galloping around the grasslands of the Ethiopian mountains on all fours, eating grass. Their overall appearance is a little sheep-like. Unsurprisingly, their hands (fore-paws?) are much like their feet, and they don’t seem to have much opposability in either pair.
Hamadryas baboons also spend a lot of time on the ground, only climbing trees for safety and when sleeping. Also they are omnivores, even predators. So their hands are much more grasping than their close cousins, the Geladas.
Marmosets and tamarins (a family of small New World Monkeys) are the only primates that have claws, instead of nails. The cute little Pygmy Marmoset below displays his claws.
Sifakas are a type of Lemur that leap feet-first, tree-to-tree. Their fore-limbs are distinctly shorter and secondary; when jumping, they grab on first with their feet. Of course, their big toes are very strong and very opposable. In the picture below, that is the big toe, all covered in whitish hair, holding the branch against the four other toes.