Solve 71!/(7+3)!

$$\frac{ 71 ! }{ (7+3) ! }$$

Evaluate

$$234369099583295391733126004254829698602453871285492789871701599258319191021296025600000000000000$$

Solution Steps

The factorial of 71 is 850478588567862317521167644239926010288584608120796235886430763388588680378079017697280000000000000000.

$$\frac{850478588567862317521167644239926010288584608120796235886430763388588680378079017697280000000000000000}{\left(7+3\right)!}$$

Add 7 and 3 to get 10.

$$\frac{850478588567862317521167644239926010288584608120796235886430763388588680378079017697280000000000000000}{10!}$$

The factorial of 10 is 3628800.

$$\frac{850478588567862317521167644239926010288584608120796235886430763388588680378079017697280000000000000000}{3628800}$$

Divide 850478588567862317521167644239926010288584608120796235886430763388588680378079017697280000000000000000 by 3628800 to get 234369099583295391733126004254829698602453871285492789871701599258319191021296025600000000000000.

$$234369099583295391733126004254829698602453871285492789871701599258319191021296025600000000000000$$

Factor

$$2^{59}\times 3^{28}\times 5^{14}\times 7^{10}\times 11^{6}\times 13^{5}\times 17^{4}\times 19^{3}\times 23^{3}\times 29^{2}\times 31^{2}\times 37\times 41\times 43\times 47\times 53\times 59\times 61\times 67\times 71$$