Finding the sharps of all musical scales

A hint is the move in steps of a 5th (in fact perfect fifth).
Also remembering that C major and A minor have all the white or natural keys.


So starting from them:


C major
C D E F G A B C
G major (one fifth above)
G A B C D E #F G
D major (one fifth above)
D E #F G A B #C D

note the sharp added is also one fifth above


Etc


Similarly from A minor:


A minor
A B C D E F G A

E minor
E #F G A B C D E


B minor
B #C D E #F G A B


Etc


See also:


Musical Acoustics - Donald Hall