Solve 6!12!/3!13!

$$\frac { 6 ! 12 ! } { 3 ! 13 ! }$$

Evaluate

$$\frac{120}{13}\approx 9.230769231$$

Solution Steps

The factorial of 6 is 720.

$$\frac{720\times 12!}{3!\times 13!}$$

The factorial of 12 is 479001600.

$$\frac{720\times 479001600}{3!\times 13!}$$

Multiply 720 and 479001600 to get 344881152000.

$$\frac{344881152000}{3!\times 13!}$$

The factorial of 3 is 6.

$$\frac{344881152000}{6\times 13!}$$

The factorial of 13 is 6227020800.

$$\frac{344881152000}{6\times 6227020800}$$

Multiply 6 and 6227020800 to get 37362124800.

$$\frac{344881152000}{37362124800}$$

Reduce the fraction \frac{344881152000}{37362124800} to lowest terms by extracting and canceling out 2874009600.

$$\frac{120}{13}$$

Factor

$$\frac{2 ^ {3} \cdot 3 \cdot 5}{13} = 9\frac{3}{13} = 9.23076923076923$$