Solve 100!/(100-20)!*20!

$$\frac{ 100 ! }{ (100-20) ! \times 20 ! }$$

Evaluate

$$535983370403809682970$$

Solution Steps

The factorial of 100 is 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000.

$$\frac{93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000}{\left(100-20\right)!\times 20!}$$

Subtract 20 from 100 to get 80.

$$\frac{93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000}{80!\times 20!}$$

The factorial of 80 is 71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000.

$$\frac{93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000}{71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000\times 20!}$$

The factorial of 20 is 2432902008176640000.

$$\frac{93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000}{71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000\times 2432902008176640000}$$

Multiply 71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000 and 2432902008176640000 to get 174121475771966982393414026414055739581071170383962456788236230253146853099637703337556165538417828496463155639091200000000000000000000000.

$$\frac{93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000}{174121475771966982393414026414055739581071170383962456788236230253146853099637703337556165538417828496463155639091200000000000000000000000}$$

Divide 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 by 174121475771966982393414026414055739581071170383962456788236230253146853099637703337556165538417828496463155639091200000000000000000000000 to get 535983370403809682970.

$$535983370403809682970$$

Factor

$$2\times 3^{4}\times 5\times 7^{2}\times 11\times 23\times 29\times 31\times 41\times 43\times 47\times 83\times 89\times 97$$