1. An information processing apparatus comprising: a free page storage unit which divides a memory region in a memory into pages of a plurality of different page sizes and manages the divided pages, and stores management information about an initialization state corresponding to an unused memory region in the memory; and a page allocating unit which selects a free page of a page size according to a requested region size or a requested page size from the free page storage unit when an allocation of the unused memory region is requested, and performs an initializing process on a memory region on which the initializing process has not been performed in a memory region corresponding to the free page using management information about the selected free page, wherein: the free page storage unit includes a page structure set in page units having a smallest page size in the plurality of different page sizes; when first and second pages having the smallest page size are free pages on which the initializing process has been performed, the page allocating unit records management information about a third page obtained by combining the first and second pages in the page structure corresponding to the first page; and when any of the first and second pages is a free page on which the initializing process has not been performed, the page allocating unit records the management information about the third page in each of the page structures corresponding to the first and second page.