Solve 48!+49!/23!+24!

$$\frac { 48 ! + 49 ! } { 23 ! + 24 ! }$$

Evaluate

$$960382759915503387283186325127168000000$$

Solution Steps

The factorial of 48 is 12413915592536072670862289047373375038521486354677760000000000.

$$\frac{12413915592536072670862289047373375038521486354677760000000000+49!}{23!+24!}$$

The factorial of 49 is 608281864034267560872252163321295376887552831379210240000000000.

$$\frac{12413915592536072670862289047373375038521486354677760000000000+608281864034267560872252163321295376887552831379210240000000000}{23!+24!}$$

Add 12413915592536072670862289047373375038521486354677760000000000 and 608281864034267560872252163321295376887552831379210240000000000 to get 620695779626803633543114452368668751926074317733888000000000000.

$$\frac{620695779626803633543114452368668751926074317733888000000000000}{23!+24!}$$

The factorial of 23 is 25852016738884976640000.

$$\frac{620695779626803633543114452368668751926074317733888000000000000}{25852016738884976640000+24!}$$

The factorial of 24 is 620448401733239439360000.

$$\frac{620695779626803633543114452368668751926074317733888000000000000}{25852016738884976640000+620448401733239439360000}$$

Add 25852016738884976640000 and 620448401733239439360000 to get 646300418472124416000000.

$$\frac{620695779626803633543114452368668751926074317733888000000000000}{646300418472124416000000}$$

Divide 620695779626803633543114452368668751926074317733888000000000000 by 646300418472124416000000 to get 960382759915503387283186325127168000000.

$$960382759915503387283186325127168000000$$

Factor

$$2^{28}\times 3^{13}\times 5^{6}\times 7^{3}\times 11^{2}\times 13^{2}\times 17\times 19\times 23\times 29\times 31\times 37\times 41\times 43\times 47$$