Solve 72!/4!*68!

$$\frac{ 72 ! }{ 4 ! \times 68 ! }$$

Evaluate

$$1028790$$

Solution Steps

The factorial of 72 is 61234458376886086861524070385274672740778091784697328983823014963978384987221689274204160000000000000000.

$$\frac{61234458376886086861524070385274672740778091784697328983823014963978384987221689274204160000000000000000}{4!\times 68!}$$

The factorial of 4 is 24.

$$\frac{61234458376886086861524070385274672740778091784697328983823014963978384987221689274204160000000000000000}{24\times 68!}$$

The factorial of 68 is 2480035542436830599600990418569171581047399201355367672371710738018221445712183296000000000000000.

$$\frac{61234458376886086861524070385274672740778091784697328983823014963978384987221689274204160000000000000000}{24\times 2480035542436830599600990418569171581047399201355367672371710738018221445712183296000000000000000}$$

Multiply 24 and 2480035542436830599600990418569171581047399201355367672371710738018221445712183296000000000000000 to get 59520853018483934390423770045660117945137580832528824136921057712437314697092399104000000000000000.

$$\frac{61234458376886086861524070385274672740778091784697328983823014963978384987221689274204160000000000000000}{59520853018483934390423770045660117945137580832528824136921057712437314697092399104000000000000000}$$

Divide 61234458376886086861524070385274672740778091784697328983823014963978384987221689274204160000000000000000 by 59520853018483934390423770045660117945137580832528824136921057712437314697092399104000000000000000 to get 1028790.

$$1028790$$

Factor

$$2\times 3^{2}\times 5\times 7\times 23\times 71$$