I am very proud of how I divided 3367 by 37 yesterday at #100factorial...
3367
=3330+37
=30*111+37
=30*(3*37)+37 (I happen to know the fact that 111=3*37)
=90*37+37
=91*37
Observations of this sort crowd and jostle each other in the mind of the experienced mental calculator, generally rising to prominence precisely when they're most needed. Steven B Smith's masterful survey THE GREAT MENTAL CALCULATORS documents this phenomenon in great detail.