Solve lceil1!2!3!rceilleft|2!3!4!right|lfloor3!4!5!rfloor

$$\lceil 1 ! 2 ! 3 ! \rceil \left| 2 ! 3 ! 4 ! \right| \lfloor 3 ! 4 ! 5 ! \rfloor$$

Evaluate

$$59719680$$

Solution Steps

The factorial of 1 is 1.

$$\lceil 1\times 2!\times 3!\rceil |2!\times 3!\times 4!|\lfloor 3!\times 4!\times 5!\rfloor$$

The factorial of 2 is 2.

$$\lceil 1\times 2\times 3!\rceil |2!\times 3!\times 4!|\lfloor 3!\times 4!\times 5!\rfloor$$

Multiply 1 and 2 to get 2.

$$\lceil 2\times 3!\rceil |2!\times 3!\times 4!|\lfloor 3!\times 4!\times 5!\rfloor$$

The factorial of 3 is 6.

$$\lceil 2\times 6\rceil |2!\times 3!\times 4!|\lfloor 3!\times 4!\times 5!\rfloor$$

Multiply 2 and 6 to get 12.

$$\lceil 12\rceil |2!\times 3!\times 4!|\lfloor 3!\times 4!\times 5!\rfloor$$

The ceiling of a real number a is the smallest integer number greater than or equal to a. The ceiling of 12 is 12.

$$12|2!\times 3!\times 4!|\lfloor 3!\times 4!\times 5!\rfloor$$

The factorial of 2 is 2.

$$12|2\times 3!\times 4!|\lfloor 3!\times 4!\times 5!\rfloor$$

The factorial of 3 is 6.

$$12|2\times 6\times 4!|\lfloor 3!\times 4!\times 5!\rfloor$$

Multiply 2 and 6 to get 12.

$$12|12\times 4!|\lfloor 3!\times 4!\times 5!\rfloor$$

The factorial of 4 is 24.

$$12|12\times 24|\lfloor 3!\times 4!\times 5!\rfloor$$

Multiply 12 and 24 to get 288.

$$12|288|\lfloor 3!\times 4!\times 5!\rfloor$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 288 is 288.

$$12\times 288\lfloor 3!\times 4!\times 5!\rfloor$$

Multiply 12 and 288 to get 3456.

$$3456\lfloor 3!\times 4!\times 5!\rfloor$$

The factorial of 3 is 6.

$$3456\lfloor 6\times 4!\times 5!\rfloor$$

The factorial of 4 is 24.

$$3456\lfloor 6\times 24\times 5!\rfloor$$

Multiply 6 and 24 to get 144.

$$3456\lfloor 144\times 5!\rfloor$$

The factorial of 5 is 120.

$$3456\lfloor 144\times 120\rfloor$$

Multiply 144 and 120 to get 17280.

$$3456\lfloor 17280\rfloor$$

The floor of a real number a is the largest integer number less than or equal to a. The floor of 17280 is 17280.

$$3456\times 17280$$

Multiply 3456 and 17280 to get 59719680.

$$59719680$$

Factor

$$2^{14}\times 3^{6}\times 5$$