Solve 130!/3!(130-3)!

$$\frac{ 130 ! }{ 3 ! (130-3) ! }$$

Evaluate

$$357760$$

Solution Steps

The factorial of 130 is 6466855489220473672507304395536485253155359447828049608975952322944781961185526165512707047229268452925683969240398027149120740074042105844737747799459310029635780991774612983803150965145600000000000000000000000000000000.

$$\frac{6466855489220473672507304395536485253155359447828049608975952322944781961185526165512707047229268452925683969240398027149120740074042105844737747799459310029635780991774612983803150965145600000000000000000000000000000000}{3!\left(130-3\right)!}$$

The factorial of 3 is 6.

$$\frac{6466855489220473672507304395536485253155359447828049608975952322944781961185526165512707047229268452925683969240398027149120740074042105844737747799459310029635780991774612983803150965145600000000000000000000000000000000}{6\left(130-3\right)!}$$

Subtract 3 from 130 to get 127.

$$\frac{6466855489220473672507304395536485253155359447828049608975952322944781961185526165512707047229268452925683969240398027149120740074042105844737747799459310029635780991774612983803150965145600000000000000000000000000000000}{6\times 127!}$$

The factorial of 127 is 3012660018457659544809977077527059692324164918673621799053346900596667207618480809067860692097713761984609779945772783965563851033300772326297773087851869982500270661791244122597621760000000000000000000000000000000.

$$\frac{6466855489220473672507304395536485253155359447828049608975952322944781961185526165512707047229268452925683969240398027149120740074042105844737747799459310029635780991774612983803150965145600000000000000000000000000000000}{6\times 3012660018457659544809977077527059692324164918673621799053346900596667207618480809067860692097713761984609779945772783965563851033300772326297773087851869982500270661791244122597621760000000000000000000000000000000}$$

Multiply 6 and 3012660018457659544809977077527059692324164918673621799053346900596667207618480809067860692097713761984609779945772783965563851033300772326297773087851869982500270661791244122597621760000000000000000000000000000000 to get 18075960110745957268859862465162358153944989512041730794320081403580003245710884854407164152586282571907658679674636703793383106199804633957786638527111219895001623970747464735585730560000000000000000000000000000000.

$$\frac{6466855489220473672507304395536485253155359447828049608975952322944781961185526165512707047229268452925683969240398027149120740074042105844737747799459310029635780991774612983803150965145600000000000000000000000000000000}{18075960110745957268859862465162358153944989512041730794320081403580003245710884854407164152586282571907658679674636703793383106199804633957786638527111219895001623970747464735585730560000000000000000000000000000000}$$

Divide 6466855489220473672507304395536485253155359447828049608975952322944781961185526165512707047229268452925683969240398027149120740074042105844737747799459310029635780991774612983803150965145600000000000000000000000000000000 by 18075960110745957268859862465162358153944989512041730794320081403580003245710884854407164152586282571907658679674636703793383106199804633957786638527111219895001623970747464735585730560000000000000000000000000000000 to get 357760.

$$357760$$

Factor

$$2^{7}\times 5\times 13\times 43$$