5!/312!= పరిష్కరించండి

$$\frac { 5 ! } { 312 ! } =$$

మూల్యాంకనం చేయండి

$$\frac{1}{1751688837605315299459772035099642780225365906000001396139640356071743969707250593966821940833910705839735841982818842509783011908504923072080611614544585244724174414358493647891739481046856056197344431809811652635921657742497007934557826539554676795285154837305935076372748668489255092849980071300679309284599817321080413964634988982508116299675736471589734895376559678022668526729217349077339472219790193382096412889437612241261766597841913827848020934872710889923082700536268756398110627818730653544871318049002473658244673970433193260022717462639039806918883278848000000000000000000000000000000000000000000000000000000000000000000000000000}\approx 5.708776459 \cdot 10^{-643}$$

పరిష్కారం దశలు

5 యొక్క క్రమ గణితము 120.

$$\frac{120}{312!}$$

312 యొక్క క్రమ గణితము 210202660512637835935172644211957133627043908720000167536756842728609276364870071276018632900069284700768301037938261101173961429020590768649673393745350229366900929723019237747008737725622726743681331817177398316310598929099640952146939184746561215434218580476712209164729840218710611141997608556081517114151978078529649675756198677900973955961088376590768187445187161362720223207506081889280736666374823205851569546732513468951411991741029659341762512184725306790769924064352250767773275338247678425384558165880296838989360876451983191202726095516684776830265993461760000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{120}{210202660512637835935172644211957133627043908720000167536756842728609276364870071276018632900069284700768301037938261101173961429020590768649673393745350229366900929723019237747008737725622726743681331817177398316310598929099640952146939184746561215434218580476712209164729840218710611141997608556081517114151978078529649675756198677900973955961088376590768187445187161362720223207506081889280736666374823205851569546732513468951411991741029659341762512184725306790769924064352250767773275338247678425384558165880296838989360876451983191202726095516684776830265993461760000000000000000000000000000000000000000000000000000000000000000000000000000}$$

120ని సంగ్రహించడం మరియు తీసివేయడం కోసం \frac{120}{210202660512637835935172644211957133627043908720000167536756842728609276364870071276018632900069284700768301037938261101173961429020590768649673393745350229366900929723019237747008737725622726743681331817177398316310598929099640952146939184746561215434218580476712209164729840218710611141997608556081517114151978078529649675756198677900973955961088376590768187445187161362720223207506081889280736666374823205851569546732513468951411991741029659341762512184725306790769924064352250767773275338247678425384558165880296838989360876451983191202726095516684776830265993461760000000000000000000000000000000000000000000000000000000000000000000000000000} యొక్క భిన్నమును అత్యంత తక్కువ విలువలకు తగ్గించండి.

$$\frac{1}{1751688837605315299459772035099642780225365906000001396139640356071743969707250593966821940833910705839735841982818842509783011908504923072080611614544585244724174414358493647891739481046856056197344431809811652635921657742497007934557826539554676795285154837305935076372748668489255092849980071300679309284599817321080413964634988982508116299675736471589734895376559678022668526729217349077339472219790193382096412889437612241261766597841913827848020934872710889923082700536268756398110627818730653544871318049002473658244673970433193260022717462639039806918883278848000000000000000000000000000000000000000000000000000000000000000000000000000}$$

లబ్ధమూలము

$$\frac{1}{2^{305}\times 3^{152}\times 5^{75}\times 7^{50}\times 11^{30}\times 13^{25}\times 17^{19}\times 19^{16}\times 23^{13}\times 29^{10}\times 31^{10}\times 37^{8}\times 41^{7}\times 43^{7}\times 47^{6}\times 53^{5}\times 59^{5}\times 61^{5}\times 67^{4}\times 71^{4}\times 73^{4}\times 79^{3}\times 83^{3}\times 89^{3}\times 97^{3}\times 101^{3}\times 103^{3}\times 107^{2}\times 109^{2}\times 113^{2}\times 127^{2}\times 131^{2}\times 137^{2}\times 139^{2}\times 149^{2}\times 151^{2}\times 157\times 163\times 167\times 173\times 179\times 181\times 191\times 193\times 197\times 199\times 211\times 223\times 227\times 229\times 233\times 239\times 241\times 251\times 257\times 263\times 269\times 271\times 277\times 281\times 283\times 293\times 307\times 311}$$