Solve 20!div(3!)div(5!)div(10!)

$$20 ! \div (3 ! ) \div (5 ! ) \div (10 ! )$$

Evaluate

$$931170240$$

Solution Steps

The factorial of 20 is 2432902008176640000.

$$\frac{\frac{\frac{2432902008176640000}{3!}}{5!}}{10!}$$

The factorial of 3 is 6.

$$\frac{\frac{\frac{2432902008176640000}{6}}{5!}}{10!}$$

Divide 2432902008176640000 by 6 to get 405483668029440000.

$$\frac{\frac{405483668029440000}{5!}}{10!}$$

The factorial of 5 is 120.

$$\frac{\frac{405483668029440000}{120}}{10!}$$

Divide 405483668029440000 by 120 to get 3379030566912000.

$$\frac{3379030566912000}{10!}$$

The factorial of 10 is 3628800.

$$\frac{3379030566912000}{3628800}$$

Divide 3379030566912000 by 3628800 to get 931170240.

$$931170240$$

Factor

$$2^{6}\times 3^{2}\times 5\times 7\times 11\times 13\times 17\times 19$$