Resolver 30!div4!div26!*10/40!div5!div35!

$$\frac{ 30 ! \div 4 ! \div 26 ! \times 10 }{ 40 ! \div 5 ! \div 35 ! }$$

Avaliar

$$\frac{15225}{36556}\approx 0,416484298$$

Passos Para a Resolução

O fatorial de 30 é 265252859812191058636308480000000.

$$\frac{\frac{\frac{265252859812191058636308480000000}{4!}}{26!}\times 10}{\frac{\frac{40!}{5!}}{35!}}$$

O fatorial de 4 é 24.

$$\frac{\frac{\frac{265252859812191058636308480000000}{24}}{26!}\times 10}{\frac{\frac{40!}{5!}}{35!}}$$

Dividir 265252859812191058636308480000000 por 24 para obter 11052202492174627443179520000000.

$$\frac{\frac{11052202492174627443179520000000}{26!}\times 10}{\frac{\frac{40!}{5!}}{35!}}$$

O fatorial de 26 é 403291461126605635584000000.

$$\frac{\frac{11052202492174627443179520000000}{403291461126605635584000000}\times 10}{\frac{\frac{40!}{5!}}{35!}}$$

Dividir 11052202492174627443179520000000 por 403291461126605635584000000 para obter 27405.

$$\frac{27405\times 10}{\frac{\frac{40!}{5!}}{35!}}$$

Multiplique 27405 e 10 para obter 274050.

$$\frac{274050}{\frac{\frac{40!}{5!}}{35!}}$$

O fatorial de 40 é 815915283247897734345611269596115894272000000000.

$$\frac{274050}{\frac{\frac{815915283247897734345611269596115894272000000000}{5!}}{35!}}$$

O fatorial de 5 é 120.

$$\frac{274050}{\frac{\frac{815915283247897734345611269596115894272000000000}{120}}{35!}}$$

Dividir 815915283247897734345611269596115894272000000000 por 120 para obter 6799294027065814452880093913300965785600000000.

$$\frac{274050}{\frac{6799294027065814452880093913300965785600000000}{35!}}$$

O fatorial de 35 é 10333147966386144929666651337523200000000.

$$\frac{274050}{\frac{6799294027065814452880093913300965785600000000}{10333147966386144929666651337523200000000}}$$

Dividir 6799294027065814452880093913300965785600000000 por 10333147966386144929666651337523200000000 para obter 658008.

$$\frac{274050}{658008}$$

Reduza a fração \frac{274050}{658008} para os termos mais baixos ao retirar e anular 18.

$$\frac{15225}{36556}$$

Fatorizar

$$\frac{3 \cdot 5 ^ {2} \cdot 7 \cdot 29}{2 ^ {2} \cdot 13 \cdot 19 \cdot 37} = 0,41648429806324544$$