Solve 8!-8*6!+48*4!-64*3!+16*4!

$$8 ! - 8 \times 6 ! + 48 \times 4 ! - 64 \times 3 ! + 16 \times 4 !$$

Evaluate

$$35712$$

Solution Steps

The factorial of 8 is 40320.

$$40320-8\times 6!+48\times 4!-64\times 3!+16\times 4!$$

The factorial of 6 is 720.

$$40320-8\times 720+48\times 4!-64\times 3!+16\times 4!$$

Multiply 8 and 720 to get 5760.

$$40320-5760+48\times 4!-64\times 3!+16\times 4!$$

Subtract 5760 from 40320 to get 34560.

$$34560+48\times 4!-64\times 3!+16\times 4!$$

The factorial of 4 is 24.

$$34560+48\times 24-64\times 3!+16\times 4!$$

Multiply 48 and 24 to get 1152.

$$34560+1152-64\times 3!+16\times 4!$$

Add 34560 and 1152 to get 35712.

$$35712-64\times 3!+16\times 4!$$

The factorial of 3 is 6.

$$35712-64\times 6+16\times 4!$$

Multiply 64 and 6 to get 384.

$$35712-384+16\times 4!$$

Subtract 384 from 35712 to get 35328.

$$35328+16\times 4!$$

The factorial of 4 is 24.

$$35328+16\times 24$$

Multiply 16 and 24 to get 384.

$$35328+384$$

Add 35328 and 384 to get 35712.

$$35712$$

Factor

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