The upper-right number on a check that you keep track of checks written is called a

Check number.

The check number (7 in the figure) appears on the check twice: once in the upper right corner, and once at the bottom in magnetic ink.

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When you order checks, the check numbers in your order are all different. If you use the reorder form supplied, it has information that allows the check printer to make sure new checks start with a sequential number after the last of the old checks.