With any note as a starting point, a certain series of intervals produces a major scale: whole step, whole, half, whole, whole, whole, half. Starting on C, this yields C-D-E-F-G-A-B-C (a C-major scale). There are no sharps or flats in this scale, so the key signature for C has no sharps or flats in it.
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Answer:
With any note as a starting point, a certain series of intervals produces a major scale: whole step, whole, half, whole, whole, whole, half. Starting on C, this yields C-D-E-F-G-A-B-C (a C-major scale). There are no sharps or flats in this scale, so the key signature for C has no sharps or flats in it.