Solve 52!/(5!)(47)!

$$\frac{ 52 ! }{ (5 ! )(47) ! }$$

Evaluate

$$2598960$$

Solution Steps

The factorial of 52 is 80658175170943878571660636856403766975289505440883277824000000000000.

$$\frac{80658175170943878571660636856403766975289505440883277824000000000000}{5!\times 47!}$$

The factorial of 5 is 120.

$$\frac{80658175170943878571660636856403766975289505440883277824000000000000}{120\times 47!}$$

The factorial of 47 is 258623241511168180642964355153611979969197632389120000000000.

$$\frac{80658175170943878571660636856403766975289505440883277824000000000000}{120\times 258623241511168180642964355153611979969197632389120000000000}$$

Multiply 120 and 258623241511168180642964355153611979969197632389120000000000 to get 31034788981340181677155722618433437596303715886694400000000000.

$$\frac{80658175170943878571660636856403766975289505440883277824000000000000}{31034788981340181677155722618433437596303715886694400000000000}$$

Divide 80658175170943878571660636856403766975289505440883277824000000000000 by 31034788981340181677155722618433437596303715886694400000000000 to get 2598960.

$$2598960$$

Factor

$$2^{4}\times 3\times 5\times 7^{2}\times 13\times 17$$