What is the value of \( 7! \) (7 factorial)?

To calculate the value of ( 7! ), we need to understand the definition of factorial. The factorial of a number ( n ), denoted ( n! ), is the product of all positive integers from 1 to ( n ). Thus, for ( 7! ), we compute:

[

7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1

]

Breaking this down step by step:

1. Calculate ( 7 \times 6 = 42 ).

2. Next, ( 42 \times 5 = 210 ).

3. Then, ( 210 \times 4 = 840 ).

4. Continuing, ( 840 \times 3 = 2520 ).

5. Next, ( 2520 \times 2 = 5040 ).

6. Finally, ( 5040 \times 1 = 5040 ).

Each multiplication step consistently builds on the previous total.

Thus, ( 7! = 5040 ), confirming that the value of ( 7! ) is indeed 5040. This makes the choice of