To compute the value of [tex]\( 5! \)[/tex], known as "5 factorial," follow these steps:
1. Understand the meaning of factorial: For any positive integer [tex]\( n \)[/tex], the factorial [tex]\( n! \)[/tex] is defined as the product of all positive integers from 1 to [tex]\( n \)[/tex].
2. List the range of numbers to multiply: Since we want to find [tex]\( 5! \)[/tex],
[tex]\[
5! = 5 \times 4 \times 3 \times 2 \times 1
\][/tex]
3. Perform the multiplications step-by-step:
- Step 1: Start with the first two numbers: [tex]\( 5 \times 4 = 20 \)[/tex]
- Step 2: Multiply the result by the next number: [tex]\( 20 \times 3 = 60 \)[/tex]
- Step 3: Continue with the next number: [tex]\( 60 \times 2 = 120 \)[/tex]
- Step 4: Finally, multiply by 1 (though multiplying by 1 does not change the result): [tex]\( 120 \times 1 = 120 \)[/tex]
4. Combine the results: By multiplying these numbers sequentially, we obtain:
[tex]\[
5! = 120
\][/tex]
Thus, the value of [tex]\( 5! \)[/tex] (5 factorial) is [tex]\( \boxed{120} \)[/tex].
