1. Stating the problem: Calculate the factorial of 6, denoted as $6!$. 2. Factorial definition: The factorial of a positive integer $n$ is the product of all positive integers from 1 up to $n$, i.e., $$n! = n imes (n-1) imes (n-2) imes \cdots \times 2 \times 1$$ 3. Apply the definition to $6!$: $$6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1$$ 4. Calculate step-by-step: $$6 \times 5 = 30$$ $$30 \times 4 = 120$$ $$120 \times 3 = 360$$ $$360 \times 2 = 720$$ $$720 \times 1 = 720$$ 5. Final answer: $$6! = 720$$