Solve 211!/112!*1/1000000000000000000000000000000000000000000000000000000

$$\frac{ 211 ! }{ 112 ! } \times \frac{ 1 }{ 1000000000000000000000000000000000000000000000000000000 }$$

Evaluate

$$\frac{21063791616271550090974432029216012617308604845348385280754592257472433810642686804836799722054885086358836106959149427524472120771229520986054842060965853563750542330233670838519857152}{186264514923095703125}\approx 1.130853702 \cdot 10^{164}$$

Solution Steps

The factorial of 211 is 22328783881661914958481873975346502495151470121092663127656427617172486869336444341196216861471796204456103981797935323465763492125980526669772652700063306391000092324747490987759008282321662774044560021923711172537165034028116470777032463317525690139861312277154265627409161865934581816407380706408159413469087649804140238680046340298380454769197056000000000000000000000000000000000000000000000000000.

$$\frac{22328783881661914958481873975346502495151470121092663127656427617172486869336444341196216861471796204456103981797935323465763492125980526669772652700063306391000092324747490987759008282321662774044560021923711172537165034028116470777032463317525690139861312277154265627409161865934581816407380706408159413469087649804140238680046340298380454769197056000000000000000000000000000000000000000000000000000}{112!}\times \frac{1}{1000000000000000000000000000000000000000000000000000000}$$

The factorial of 112 is 197450685722107402353682037275992488341277868034975337796656295094902858969771811440894224355027779366597957338237853638272334919686385621811850780464277094400000000000000000000000000.

$$\frac{22328783881661914958481873975346502495151470121092663127656427617172486869336444341196216861471796204456103981797935323465763492125980526669772652700063306391000092324747490987759008282321662774044560021923711172537165034028116470777032463317525690139861312277154265627409161865934581816407380706408159413469087649804140238680046340298380454769197056000000000000000000000000000000000000000000000000000}{197450685722107402353682037275992488341277868034975337796656295094902858969771811440894224355027779366597957338237853638272334919686385621811850780464277094400000000000000000000000000}\times \frac{1}{1000000000000000000000000000000000000000000000000000000}$$

Divide 22328783881661914958481873975346502495151470121092663127656427617172486869336444341196216861471796204456103981797935323465763492125980526669772652700063306391000092324747490987759008282321662774044560021923711172537165034028116470777032463317525690139861312277154265627409161865934581816407380706408159413469087649804140238680046340298380454769197056000000000000000000000000000000000000000000000000000 by 197450685722107402353682037275992488341277868034975337796656295094902858969771811440894224355027779366597957338237853638272334919686385621811850780464277094400000000000000000000000000 to get 113085370152056611369951262922072113388579776687698065634060939934573643547793745710430986779409526703686671000016880998993412497970241362931064023392866974036292038013271560361839604393039626240000000000000000000000000.

$$113085370152056611369951262922072113388579776687698065634060939934573643547793745710430986779409526703686671000016880998993412497970241362931064023392866974036292038013271560361839604393039626240000000000000000000000000\times \frac{1}{1000000000000000000000000000000000000000000000000000000}$$

Multiply 113085370152056611369951262922072113388579776687698065634060939934573643547793745710430986779409526703686671000016880998993412497970241362931064023392866974036292038013271560361839604393039626240000000000000000000000000 and \frac{1}{1000000000000000000000000000000000000000000000000000000} to get \frac{113085370152056611369951262922072113388579776687698065634060939934573643547793745710430986779409526703686671000016880998993412497970241362931064023392866974036292038013271560361839604393039626240000000000000000000000000}{1000000000000000000000000000000000000000000000000000000}.

$$\frac{113085370152056611369951262922072113388579776687698065634060939934573643547793745710430986779409526703686671000016880998993412497970241362931064023392866974036292038013271560361839604393039626240000000000000000000000000}{1000000000000000000000000000000000000000000000000000000}$$

Reduce the fraction \frac{113085370152056611369951262922072113388579776687698065634060939934573643547793745710430986779409526703686671000016880998993412497970241362931064023392866974036292038013271560361839604393039626240000000000000000000000000}{1000000000000000000000000000000000000000000000000000000} to lowest terms by extracting and canceling out 5368709120000000000000000000000000.

$$\frac{21063791616271550090974432029216012617308604845348385280754592257472433810642686804836799722054885086358836106959149427524472120771229520986054842060965853563750542330233670838519857152}{186264514923095703125}$$

Factor

$$\frac{2^{43}\times 3^{48}\times 7^{16}\times 11^{10}\times 13^{9}\times 17^{6}\times 19^{6}\times 23^{5}\times 29^{4}\times 31^{3}\times 37^{2}\times 41^{3}\times 43^{2}\times 47^{2}\times 53\times 59^{2}\times 61^{2}\times 67^{2}\times 71\times 73\times 79\times 83\times 89\times 97\times 101\times 103\times 113\times 127\times 131\times 137\times 139\times 149\times 151\times 157\times 163\times 167\times 173\times 179\times 181\times 191\times 193\times 197\times 199\times 211}{5^{29}}$$