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

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

Evaluate

$$\frac{1}{258623241511168180642964355153611979969197632389120000000000}\approx 3.866628514 \cdot 10^{-60}$$

Solution Steps

The factorial of 52 is 80658175170943878571660636856403766975289505440883277824000000000000.

$$\frac{80658175170943878571660636856403766975289505440883277824000000000000}{52!\times 47!}$$

The factorial of 52 is 80658175170943878571660636856403766975289505440883277824000000000000.

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

The factorial of 47 is 258623241511168180642964355153611979969197632389120000000000.

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

Multiply 80658175170943878571660636856403766975289505440883277824000000000000 and 258623241511168180642964355153611979969197632389120000000000 to get 20860078717085127561426227534196968755024141269412279518679263152567054706993536327731294908575413834874880000000000000000000000.

$$\frac{80658175170943878571660636856403766975289505440883277824000000000000}{20860078717085127561426227534196968755024141269412279518679263152567054706993536327731294908575413834874880000000000000000000000}$$

Reduce the fraction \frac{80658175170943878571660636856403766975289505440883277824000000000000}{20860078717085127561426227534196968755024141269412279518679263152567054706993536327731294908575413834874880000000000000000000000} to lowest terms by extracting and canceling out 80658175170943878571660636856403766975289505440883277824000000000000.

$$\frac{1}{258623241511168180642964355153611979969197632389120000000000}$$

Factor

$$\frac{1}{2 ^ {42} \cdot 3 ^ {21} \cdot 5 ^ {10} \cdot 7 ^ {6} \cdot 11 ^ {4} \cdot 13 ^ {3} \cdot 17 ^ {2} \cdot 19 ^ {2} \cdot 23 ^ {2} \cdot 29 \cdot 31 \cdot 37 \cdot 41 \cdot 43 \cdot 47} = 3.866628513960594 \times 10^{-60}$$