These are viral warts as described by you, requires procedure ie RF cautery procedure, in which the lesions are burnt and the base is cauterized with chemical like carbolic acid so that the warts don't reappear at the same site.
Next Steps
It is advised that the warty lesion should not be scratched or cut it may reoccur at the same place.
Health Tips
Don't burn the lesions or shave it off yourself.