RWG:My objective, more clearly stated, is ultimately to automatically simplify factorials(n/d), not just factorials(n/24), by canonicalizing first to minimal d and then to minimal n. So far, reduction is possible for n/d, n>d/2 (by reflection) 1/2, 1/6, 3/8, 4/9, n/10, n/12, n/14, n/15, n>1 5/16, 7/16, n/18, n/20, n>1 n/21, n>2 n/22, n/24, n>1 11/25, 12/25, n prime, apparently never for prime>2n It would be amazing to find a reduction inaccessible via reflection and tuplication. But how could we tell? --In fact, Chowla & Selberg *DID* find cases inaccessible by reflection and tuplication, all (n/24)! can be expressed in close form in terms of elliptic functions. No? There's been followup work by other authors. I've posted about this in the past on math-fun, you should check the archives, I think the cites are there.