1. A storage device comprising: a host interface connected to a host; a memory including: a first buffer that stores a logical address range designated by an invalidation instruction received from the host via the host interface; and a second buffer that stores an internal logical address range which is an area combination with the logical address range; a nonvolatile memory; and a controller including: an invalidation instruction processor that stores the logical address range designated by the invalidation instruction in the first buffer; an area combination executor that generates the internal logical address range by the area combination with the logical address range and stores the internal logical address range in the second buffer; and an invalidation executor that executes invalidation processing on the nonvolatile memory based on the internal logical address range.