A naturalization number refers to a C-File number, which refers to the certificate file number printed in red on a U.S. Certificate of Naturalization. C-File numbers have been provided since 1906, according to the U.S. Citizenship and Immigration Services website.
A Certificate of Naturalization is provided once an immigrant has attained U.S. citizenship, according to USCIS. As such, these documents are used to obtain U.S. passports and various state identification documents, notes the U.S. Department of State. C-File numbers can also be used when submitting certificate replacement requests and are associated in some cases with other immigration records, including court documents. Prior to the government's use of Certificates of Naturalization, C-File numbers were also used on Certificates of Citizenship.