Running this program

   10   V$="1234567890":H$=V$
   15   repeat
   20    Twos=left(V$,3):Cups=mid(V$,4,3)
   30    Two=val(Twos):Cup=val(Cups)
   40    if left(Twos,1)<>"0" and left(Cups)<>"0" and mid(V$,9,1)<>"0" then
   50      :T=left(V$,1)
   60      :E=mid(V$,7,1)
   70      :A=mid(V$,8,1)
   80      :S=mid(V$,9,1)
   90      :Teaset=val(T+E+A+S+E+T)
  100      :Tea=val(T+E+A)
  110      :Setv=val(S+E+T)
  120      :if prmdiv(Two)=Two and prmdiv(Cup)=Cup and prmdiv(Tea)=Tea and prmdiv(Setv)=Setv and Two*Cup=Teaset then
  130          :print Two;Cup;Teaset,
  210          :S$="":N=abs(Teaset)
  220          :if N>0 then Limit=sqrt(N):else Limit=0:endif
  230          :if Limit<>int(Limit) then Limit=int(Limit+1):endif
  240          :Dv=2:gosub *DivideIt
  250          :Dv=3:gosub *DivideIt
  260          :Dv=5:gosub *DivideIt
  270          :Dv=7
  280          :loop
  290          :if Dv>Limit then goto 400:endif
  300          :gosub *DivideIt:Dv=Dv+4 '11
  310          :gosub *DivideIt:Dv=Dv+2 '13
  320          :gosub *DivideIt:Dv=Dv+4 '17
  330          :gosub *DivideIt:Dv=Dv+2 '19
  340          :gosub *DivideIt:Dv=Dv+4 '23
  350          :gosub *DivideIt:Dv=Dv+6 '29
  360          :gosub *DivideIt:Dv=Dv+2 '31
  370          :gosub *DivideIt:Dv=Dv+6 '37
  380          :if inkey=chr(27) then S$=chr(27):end:endif
  390          :endloop
  400          :'
  410          :if N>1 then S$=S$+str(N):endif
  420          :print S$
  520   gosub *Permute(&V$)
  535   until V$=H$
  540   end
  800

produces no output. The factoring of the answer was in case that helped figure a property of TEASET, but no teaset was found to factor.

I've checked my logic but don't see a bug.