Solve 75!/100!

$$\frac { 75 ! } { 100 ! }$$

Evaluate

$$\frac{1}{3761767332187389431968739190317715670695936000000}\approx 2.658324962 \cdot 10^{-49}$$

Solution Steps

The factorial of 75 is 24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000.

$$\frac{24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000}{100!}$$

The factorial of 100 is 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000.

$$\frac{24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000}{93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000}$$

Reduce the fraction \frac{24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000}{93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000} to lowest terms by extracting and canceling out 24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000.

$$\frac{1}{3761767332187389431968739190317715670695936000000}$$

Factor

$$\frac{1}{2 ^ {26} \cdot 3 ^ {13} \cdot 5 ^ {6} \cdot 7 ^ {5} \cdot 11 ^ {3} \cdot 13 ^ {2} \cdot 17 \cdot 19 ^ {2} \cdot 23 \cdot 29 \cdot 31 \cdot 41 \cdot 43 \cdot 47 \cdot 79 \cdot 83 \cdot 89 \cdot 97} = 2.6583249618963554 \times 10^{-49}$$