Solve 13!/4!4!2!3!

$$\frac{ 13 ! }{ 4 ! 4 ! 2 ! 3 ! }$$

Evaluate

$$900900$$

Solution Steps

Multiply 4! and 4! to get \left(4!\right)^{2}.

$$\frac{13!}{\left(4!\right)^{2}\times 2!\times 3!}$$

The factorial of 13 is 6227020800.

$$\frac{6227020800}{\left(4!\right)^{2}\times 2!\times 3!}$$

The factorial of 4 is 24.

$$\frac{6227020800}{24^{2}\times 2!\times 3!}$$

Calculate 24 to the power of 2 and get 576.

$$\frac{6227020800}{576\times 2!\times 3!}$$

The factorial of 2 is 2.

$$\frac{6227020800}{576\times 2\times 3!}$$

Multiply 576 and 2 to get 1152.

$$\frac{6227020800}{1152\times 3!}$$

The factorial of 3 is 6.

$$\frac{6227020800}{1152\times 6}$$

Multiply 1152 and 6 to get 6912.

$$\frac{6227020800}{6912}$$

Divide 6227020800 by 6912 to get 900900.

$$900900$$

Factor

$$2^{2}\times 3^{2}\times 5^{2}\times 7\times 11\times 13$$