The complete GTIN-13 is 6291041500213. Treat 629104150021 as the twelve-digit body and 3 as the supplied check digit. Recalculating from the body makes this example independently auditable.
Multiply by 1 and 3 across the body
From left to right for this twelve-digit body, the weights are 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3. The products are 6, 6, 9, 3, 0, 12, 1, 15, 0, 0, 2, and 3. This is equivalent to starting at the rightmost data digit with weight 3.
The weighted sum is 57
Adding the twelve products gives 57. Its remainder modulo ten is 7. The difference to the next multiple of ten is 60 − 57 = 3, equivalently (10 − 7) mod 10 = 3.
Append 3 to make 6291041500213
The calculated check digit equals the supplied final digit 3, so 6291041500213 passes the GTIN-13 length and Mod-10 check. This result does not look up the trade item, identify its owner, or establish authenticity.