Solve 52!/40!(52!-40!)

$$\frac { 52 ! } { 40 ! ( 52 ! - 40 ! ) }$$

Evaluate

$$\frac{82861}{67607556285204054164927796495613096028509569024000000}\approx 1.225617439 \cdot 10^{-48}$$

Solution Steps

The factorial of 52 is 80658175170943878571660636856403766975289505440883277824000000000000.

$$\frac{80658175170943878571660636856403766975289505440883277824000000000000}{40!\left(52!-40!\right)}$$

The factorial of 40 is 815915283247897734345611269596115894272000000000.

$$\frac{80658175170943878571660636856403766975289505440883277824000000000000}{815915283247897734345611269596115894272000000000\left(52!-40!\right)}$$

The factorial of 52 is 80658175170943878571660636856403766975289505440883277824000000000000.

$$\frac{80658175170943878571660636856403766975289505440883277824000000000000}{815915283247897734345611269596115894272000000000\left(80658175170943878571660636856403766975289505440883277824000000000000-40!\right)}$$

The factorial of 40 is 815915283247897734345611269596115894272000000000.

$$\frac{80658175170943878571660636856403766975289505440883277824000000000000}{815915283247897734345611269596115894272000000000\left(80658175170943878571660636856403766975289505440883277824000000000000-815915283247897734345611269596115894272000000000\right)}$$

Subtract 815915283247897734345611269596115894272000000000 from 80658175170943878571660636856403766975289505440883277824000000000000 to get 80658175170943878570844721573155869240943894171287161929728000000000.

$$\frac{80658175170943878571660636856403766975289505440883277824000000000000}{815915283247897734345611269596115894272000000000\times 80658175170943878570844721573155869240943894171287161929728000000000}$$

Multiply 815915283247897734345611269596115894272000000000 and 80658175170943878570844721573155869240943894171287161929728000000000 to get 65810237840859226942576831014437067221708375082951461396552090222845665145588757783884679941718016000000000000000000.

$$\frac{80658175170943878571660636856403766975289505440883277824000000000000}{65810237840859226942576831014437067221708375082951461396552090222845665145588757783884679941718016000000000000000000}$$

Reduce the fraction \frac{80658175170943878571660636856403766975289505440883277824000000000000}{65810237840859226942576831014437067221708375082951461396552090222845665145588757783884679941718016000000000000000000} to lowest terms by extracting and canceling out 973415420655602497817557558518528221663864851267584000000000000.

$$\frac{82861}{67607556285204054164927796495613096028509569024000000}$$

Factor

$$\frac{41 \cdot 43 \cdot 47}{2 ^ {27} \cdot 3 ^ {13} \cdot 5 ^ {6} \cdot 7 ^ {2} \cdot 11 ^ {2} \cdot 13 ^ {2} \cdot 17 \cdot 19 ^ {2} \cdot 29 \cdot 31 \cdot 37 \cdot 98856066097780991999} = 1.2256174391283858 \times 10^{-48}$$