Solve 52!/(52-5)*(5!)

$$\frac { 52 ! } { ( 52 - 5 ) \cdot ( 5 ! ) }$$

Evaluate

$$14301094888465226697102949797234710456611614439872921600000000000$$

Solution Steps

The factorial of 52 is 80658175170943878571660636856403766975289505440883277824000000000000.

$$\frac{80658175170943878571660636856403766975289505440883277824000000000000}{\left(52-5\right)\times 5!}$$

Subtract 5 from 52 to get 47.

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

The factorial of 5 is 120.

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

Multiply 47 and 120 to get 5640.

$$\frac{80658175170943878571660636856403766975289505440883277824000000000000}{5640}$$

Divide 80658175170943878571660636856403766975289505440883277824000000000000 by 5640 to get 14301094888465226697102949797234710456611614439872921600000000000.

$$14301094888465226697102949797234710456611614439872921600000000000$$

Factor

$$2^{46}\times 3^{22}\times 5^{11}\times 7^{8}\times 11^{4}\times 13^{4}\times 17^{3}\times 19^{2}\times 23^{2}\times 29\times 31\times 37\times 41\times 43$$