If it was only bran, it would not contain gluten. Gluten is found in the wheat kernel which is below the bran, or seed coat. However, bran cannot be produced without some cross-contamination by the processing to remove the bran from the wheat grain.So, cross-contamination occurs, making it wise for people with gluten allergies to avoid wheat bran.
You can even find gluten contamination in oat products (which is free of gluten), because of the use of similar equipment and locations for processing grains. See the reference below, but you can find other references easily by looking for "gluten cross contamination.
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