Solve 100!div85!

$$100 ! \div 85 !$$

Evaluate

$$331284225412682501619179520000$$

Solution Steps

The factorial of 100 is 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000.

$$\frac{93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000}{85!}$$

The factorial of 85 is 281710411438055027694947944226061159480056634330574206405101912752560026159795933451040286452340924018275123200000000000000000000.

$$\frac{93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000}{281710411438055027694947944226061159480056634330574206405101912752560026159795933451040286452340924018275123200000000000000000000}$$

Divide 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 by 281710411438055027694947944226061159480056634330574206405101912752560026159795933451040286452340924018275123200000000000000000000 to get 331284225412682501619179520000.

$$331284225412682501619179520000$$

Factor

$$2^{16}\times 3^{7}\times 5^{4}\times 7^{3}\times 11^{2}\times 13\times 19\times 23\times 29\times 31\times 43\times 47\times 89\times 97$$