Solve 72!*3!/70!

$$\frac { 72 ! \cdot 3 ! } { 70 ! }$$

Evaluate

$$30672$$

Solution Steps

The factorial of 72 is 61234458376886086861524070385274672740778091784697328983823014963978384987221689274204160000000000000000.

$$\frac{61234458376886086861524070385274672740778091784697328983823014963978384987221689274204160000000000000000\times 3!}{70!}$$

The factorial of 3 is 6.

$$\frac{61234458376886086861524070385274672740778091784697328983823014963978384987221689274204160000000000000000\times 6}{70!}$$

Multiply 61234458376886086861524070385274672740778091784697328983823014963978384987221689274204160000000000000000 and 6 to get 367406750261316521169144422311648036444668550708183973902938089783870309923330135645224960000000000000000.

$$\frac{367406750261316521169144422311648036444668550708183973902938089783870309923330135645224960000000000000000}{70!}$$

The factorial of 70 is 11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000.

$$\frac{367406750261316521169144422311648036444668550708183973902938089783870309923330135645224960000000000000000}{11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000}$$

Divide 367406750261316521169144422311648036444668550708183973902938089783870309923330135645224960000000000000000 by 11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000 to get 30672.

$$30672$$

Factor

$$2^{4}\times 3^{3}\times 71$$