Solve 49!/(49-6)!*6!

$$\frac{ 49 ! }{ (49-6) ! \times 6 ! }$$

Evaluate

$$13983816$$

Solution Steps

The factorial of 49 is 608281864034267560872252163321295376887552831379210240000000000.

$$\frac{608281864034267560872252163321295376887552831379210240000000000}{\left(49-6\right)!\times 6!}$$

Subtract 6 from 49 to get 43.

$$\frac{608281864034267560872252163321295376887552831379210240000000000}{43!\times 6!}$$

The factorial of 43 is 60415263063373835637355132068513997507264512000000000.

$$\frac{608281864034267560872252163321295376887552831379210240000000000}{60415263063373835637355132068513997507264512000000000\times 6!}$$

The factorial of 6 is 720.

$$\frac{608281864034267560872252163321295376887552831379210240000000000}{60415263063373835637355132068513997507264512000000000\times 720}$$

Multiply 60415263063373835637355132068513997507264512000000000 and 720 to get 43498989405629161658895695089330078205230448640000000000.

$$\frac{608281864034267560872252163321295376887552831379210240000000000}{43498989405629161658895695089330078205230448640000000000}$$

Divide 608281864034267560872252163321295376887552831379210240000000000 by 43498989405629161658895695089330078205230448640000000000 to get 13983816.

$$13983816$$

Factor

$$2^{3}\times 3\times 7^{2}\times 11\times 23\times 47$$