It’s for identification. The FDA has a list of certified colorings that are allowed to be used in food. Countries other than the US use different numbering systems.
FD&C Blue No.1 has had many names. It’s full chemical name is disodium;2-[[4-[ethyl-[(3-sulfonatophenyl)methyl]amino]phenyl]-[4-[ethyl-[(3-sulfonatophenyl)methyl]azaniumylidene]cyclohexa-2,5-dien-1-ylidene]methyl]benzenesulfonate. So you can see why it might need to be identified by a number.
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