Solve 64!/61!*3!*8!/5!3!*8

$$\frac { 64 ! } { 61 ! \cdot 3 ! } \cdot \frac { 8 ! } { 5 ! 3 ! } \cdot 8$$

Evaluate

$$18665472$$

Solution Steps

The factorial of 64 is 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000.

$$\frac{126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000}{61!\times 3!}\times \frac{8!}{5!\times 3!}\times 8$$

The factorial of 61 is 507580213877224798800856812176625227226004528988036003099405939480985600000000000000.

$$\frac{126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000}{507580213877224798800856812176625227226004528988036003099405939480985600000000000000\times 3!}\times \frac{8!}{5!\times 3!}\times 8$$

The factorial of 3 is 6.

$$\frac{126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000}{507580213877224798800856812176625227226004528988036003099405939480985600000000000000\times 6}\times \frac{8!}{5!\times 3!}\times 8$$

Multiply 507580213877224798800856812176625227226004528988036003099405939480985600000000000000 and 6 to get 3045481283263348792805140873059751363356027173928216018596435636885913600000000000000.

$$\frac{126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000}{3045481283263348792805140873059751363356027173928216018596435636885913600000000000000}\times \frac{8!}{5!\times 3!}\times 8$$

Divide 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000 by 3045481283263348792805140873059751363356027173928216018596435636885913600000000000000 to get 41664.

$$41664\times \frac{8!}{5!\times 3!}\times 8$$

The factorial of 8 is 40320.

$$41664\times \frac{40320}{5!\times 3!}\times 8$$

The factorial of 5 is 120.

$$41664\times \frac{40320}{120\times 3!}\times 8$$

The factorial of 3 is 6.

$$41664\times \frac{40320}{120\times 6}\times 8$$

Multiply 120 and 6 to get 720.

$$41664\times \frac{40320}{720}\times 8$$

Divide 40320 by 720 to get 56.

$$41664\times 56\times 8$$

Multiply 41664 and 56 to get 2333184.

$$2333184\times 8$$

Multiply 2333184 and 8 to get 18665472.

$$18665472$$

Factor

$$2^{12}\times 3\times 7^{2}\times 31$$