Solve 90!/5!*85!

$$\frac { 90 ! } { 5 ! \cdot 85 ! }$$

Evaluate

$$43949268$$

Solution Steps

The factorial of 90 is 1485715964481761497309522733620825737885569961284688766942216863704985393094065876545992131370884059645617234469978112000000000000000000000.

$$\frac{1485715964481761497309522733620825737885569961284688766942216863704985393094065876545992131370884059645617234469978112000000000000000000000}{5!\times 85!}$$

The factorial of 5 is 120.

$$\frac{1485715964481761497309522733620825737885569961284688766942216863704985393094065876545992131370884059645617234469978112000000000000000000000}{120\times 85!}$$

The factorial of 85 is 281710411438055027694947944226061159480056634330574206405101912752560026159795933451040286452340924018275123200000000000000000000.

$$\frac{1485715964481761497309522733620825737885569961284688766942216863704985393094065876545992131370884059645617234469978112000000000000000000000}{120\times 281710411438055027694947944226061159480056634330574206405101912752560026159795933451040286452340924018275123200000000000000000000}$$

Multiply 120 and 281710411438055027694947944226061159480056634330574206405101912752560026159795933451040286452340924018275123200000000000000000000 to get 33805249372566603323393753307127339137606796119668904768612229530307203139175512014124834374280910882193014784000000000000000000000.

$$\frac{1485715964481761497309522733620825737885569961284688766942216863704985393094065876545992131370884059645617234469978112000000000000000000000}{33805249372566603323393753307127339137606796119668904768612229530307203139175512014124834374280910882193014784000000000000000000000}$$

Divide 1485715964481761497309522733620825737885569961284688766942216863704985393094065876545992131370884059645617234469978112000000000000000000000 by 33805249372566603323393753307127339137606796119668904768612229530307203139175512014124834374280910882193014784000000000000000000000 to get 43949268.

$$43949268$$

Factor

$$2^{2}\times 3^{2}\times 11\times 29\times 43\times 89$$