Solve 70!/(70-7)!*7!

$$\frac{ 70 ! }{ (70-7) ! \times 7 ! }$$

Evaluate

$$1198774720$$

Solution Steps

The factorial of 70 is 11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000.

$$\frac{11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000}{\left(70-7\right)!\times 7!}$$

Subtract 7 from 70 to get 63.

$$\frac{11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000}{63!\times 7!}$$

The factorial of 63 is 1982608315404440064116146708361898137544773690227268628106279599612729753600000000000000.

$$\frac{11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000}{1982608315404440064116146708361898137544773690227268628106279599612729753600000000000000\times 7!}$$

The factorial of 7 is 5040.

$$\frac{11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000}{1982608315404440064116146708361898137544773690227268628106279599612729753600000000000000\times 5040}$$

Multiply 1982608315404440064116146708361898137544773690227268628106279599612729753600000000000000 and 5040 to get 9992345909638377923145379410143966613225659398745433885655649182048157958144000000000000000.

$$\frac{11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000}{9992345909638377923145379410143966613225659398745433885655649182048157958144000000000000000}$$

Divide 11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000 by 9992345909638377923145379410143966613225659398745433885655649182048157958144000000000000000 to get 1198774720.

$$1198774720$$

Factor

$$2^{6}\times 5\times 11\times 13\times 17\times 23\times 67$$