1. The problem is to calculate the factorial of 10, denoted as $10!$. 2. The factorial of a positive integer $n$ is the product of all positive integers from 1 to $n$. The formula is: $$n! = n \times (n-1) \times (n-2) \times \cdots \times 2 \times 1$$ 3. Applying this to $10!$: $$10! = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$$ 4. Calculate step-by-step: $$10 \times 9 = 90$$ $$90 \times 8 = 720$$ $$720 \times 7 = 5040$$ $$5040 \times 6 = 30240$$ $$30240 \times 5 = 151200$$ $$151200 \times 4 = 604800$$ $$604800 \times 3 = 1814400$$ $$1814400 \times 2 = 3628800$$ $$3628800 \times 1 = 3628800$$ 5. Therefore, the value of $10!$ is: $$10! = 3628800$$