There are many causes to dropping fur. Here are some factors:

Old Age: Hamsters drop some fur when they age. If your hamster is already quite old, do not worry, unless it is dropping fur excessively, for that condition; do make a trip down to the vet to confirm your suspicions.

Ringworm, allergies: If you suspect it is this, try washing with saline water twice daily. If it does not work, do visit the vet.