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From letters F, A, C, T, O, R, A, G, E  I made following words

9 letter words

factorage[15]

7 letter words

fagoter[11], cartage[10]

6 letter words

carafe[11], factor[11], agrafe[10], forage[10], forgat[10], forget[10], carate[8], coater[8], recoat[8], agorae[7], garote[7], orgeat[7], aortae[6]

5 letter words

facer[10], farce[10], force[10], facet[10], craft[10], croft[10], forge[9], gofer[9], fagot[9], graft[9], cager[8], grace[8], afore[8], cargo[8], after[8], fetor[8], forte[8], ofter[8], areca[7], ocrea[7], aceta[7], carat[7], caret[7], carte[7], cater[7], crate[7], react[7], recta[7], trace[7], actor[7], taroc[7], recto[7], agora[6], agate[6], togae[6], gater[6], grate[6], great[6], retag[6], targe[6], terga[6], argot[6], gator[6], groat[6], ergot[6], reata[5], aorta[5], oater[5], orate[5]

4 letter words

cafe[9], face[9], corf[9], fact[9], coft[9], frag[8], frog[8], cage[7], afar[7], fare[7], fear[7], frae[7], crag[7], faro[7], fora[7], fore[7], froe[7], fate[7], feat[7], feta[7], fart[7], frat[7], raft[7], fret[7], reft[7], tref[7], fort[7], acre[6], care[6], race[6], arco[6], orca[6], cero[6], core[6], acta[6], cate[6], tace[6], coat[6], taco[6], cote[6], cart[6], torc[6], agar[5], raga[5], ager[5], gear[5], rage[5], ergo[5], goer[5], gore[5], ogre[5], gate[5], geta[5], goat[5], toga[5], grat[5], grot[5], trog[5], area[4], aero[4], toea[4], rate[4], tare[4], tear[4], rato[4], rota[4], taro[4], tora[4], rote[4], tore[4]

3 letter words

fag[7], fog[7], oaf[6], foe[6], cog[6], arf[6], far[6], fer[6], ref[6], for[6], fro[6], aft[6], fat[6], eft[6], fet[6], oft[6], ace[5], oca[5], arc[5], car[5], rec[5], cor[5], orc[5], roc[5], act[5], cat[5], cot[5], aga[4], age[4], gae[4], ago[4], goa[4], ego[4], gar[4], rag[4], erg[4], reg[4], gor[4], gat[4], tag[4], get[4], teg[4], got[4], tog[4], are[3], ear[3], era[3], oar[3], ora[3], ore[3], roe[3], ate[3], eat[3], eta[3], tae[3], tea[3], oat[3], tao[3], toe[3], art[3], rat[3], tar[3], ret[3], ort[3], rot[3]