Solve 10!div5!div5!*20!div5!div15!

$$10 ! \div 5 ! \div 5 ! \times 20 ! \div 5 ! \div 15 !$$

Evaluate

$$3907008$$

Solution Steps

The factorial of 10 is 3628800.

$$\frac{\frac{\frac{\frac{3628800}{5!}}{5!}\times 20!}{5!}}{15!}$$

The factorial of 5 is 120.

$$\frac{\frac{\frac{\frac{3628800}{120}}{5!}\times 20!}{5!}}{15!}$$

Divide 3628800 by 120 to get 30240.

$$\frac{\frac{\frac{30240}{5!}\times 20!}{5!}}{15!}$$

The factorial of 5 is 120.

$$\frac{\frac{\frac{30240}{120}\times 20!}{5!}}{15!}$$

Divide 30240 by 120 to get 252.

$$\frac{\frac{252\times 20!}{5!}}{15!}$$

The factorial of 20 is 2432902008176640000.

$$\frac{\frac{252\times 2432902008176640000}{5!}}{15!}$$

Multiply 252 and 2432902008176640000 to get 613091306060513280000.

$$\frac{\frac{613091306060513280000}{5!}}{15!}$$

The factorial of 5 is 120.

$$\frac{\frac{613091306060513280000}{120}}{15!}$$

Divide 613091306060513280000 by 120 to get 5109094217170944000.

$$\frac{5109094217170944000}{15!}$$

The factorial of 15 is 1307674368000.

$$\frac{5109094217170944000}{1307674368000}$$

Divide 5109094217170944000 by 1307674368000 to get 3907008.

$$3907008$$

Factor

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