Solve 99!/63!9!

$$\frac { 99 ! } { 63 ! 9 ! }$$

Evaluate

$$1297190317912398841992770104846676557224382081813425684480000000$$

Solution Steps

The factorial of 99 is 933262154439441526816992388562667004907159682643816214685929638952175999932299156089414639761565182862536979208272237582511852109168640000000000000000000000.

$$\frac{933262154439441526816992388562667004907159682643816214685929638952175999932299156089414639761565182862536979208272237582511852109168640000000000000000000000}{63!\times 9!}$$

The factorial of 63 is 1982608315404440064116146708361898137544773690227268628106279599612729753600000000000000.

$$\frac{933262154439441526816992388562667004907159682643816214685929638952175999932299156089414639761565182862536979208272237582511852109168640000000000000000000000}{1982608315404440064116146708361898137544773690227268628106279599612729753600000000000000\times 9!}$$

The factorial of 9 is 362880.

$$\frac{933262154439441526816992388562667004907159682643816214685929638952175999932299156089414639761565182862536979208272237582511852109168640000000000000000000000}{1982608315404440064116146708361898137544773690227268628106279599612729753600000000000000\times 362880}$$

Multiply 1982608315404440064116146708361898137544773690227268628106279599612729753600000000000000 and 362880 to get 719448905493963210466467317530365596152247476709671239767206741107467372986368000000000000000.

$$\frac{933262154439441526816992388562667004907159682643816214685929638952175999932299156089414639761565182862536979208272237582511852109168640000000000000000000000}{719448905493963210466467317530365596152247476709671239767206741107467372986368000000000000000}$$

Divide 933262154439441526816992388562667004907159682643816214685929638952175999932299156089414639761565182862536979208272237582511852109168640000000000000000000000 by 719448905493963210466467317530365596152247476709671239767206741107467372986368000000000000000 to get 1297190317912398841992770104846676557224382081813425684480000000.

$$1297190317912398841992770104846676557224382081813425684480000000$$

Factor

$$2^{31}\times 3^{14}\times 5^{7}\times 7^{5}\times 11^{4}\times 13^{3}\times 17^{2}\times 19^{2}\times 23^{2}\times 29\times 31\times 37\times 41\times 43\times 47\times 67\times 71\times 73\times 79\times 83\times 89\times 97$$