Solve =56!/(15!)*(41!)

$$= \frac { 56 ! } { ( 15 ! ) \times ( 41 ! ) }$$

Evaluate

$$16253249498640$$

Solution Steps

The factorial of 56 is 710998587804863451854045647463724949736497978881168458687447040000000000000.

$$\frac{710998587804863451854045647463724949736497978881168458687447040000000000000}{15!\times 41!}$$

The factorial of 15 is 1307674368000.

$$\frac{710998587804863451854045647463724949736497978881168458687447040000000000000}{1307674368000\times 41!}$$

The factorial of 41 is 33452526613163807108170062053440751665152000000000.

$$\frac{710998587804863451854045647463724949736497978881168458687447040000000000000}{1307674368000\times 33452526613163807108170062053440751665152000000000}$$

Multiply 1307674368000 and 33452526613163807108170062053440751665152000000000 to get 43745011596872161940650193532253917159172589223936000000000000.

$$\frac{710998587804863451854045647463724949736497978881168458687447040000000000000}{43745011596872161940650193532253917159172589223936000000000000}$$

Divide 710998587804863451854045647463724949736497978881168458687447040000000000000 by 43745011596872161940650193532253917159172589223936000000000000 to get 16253249498640.

$$16253249498640$$

Factor

$$2^{4}\times 3^{2}\times 5\times 7^{2}\times 11\times 17\times 23\times 43\times 47\times 53$$