1. **State the problem:** We are given the product of three numbers is 1197, and two of the numbers are 3 and 19. We need to find the third number. 2. **Formula and rule:** The product of three numbers $a$, $b$, and $c$ is given by $$a \times b \times c = \text{product}.$$ Here, $a=3$, $b=19$, and the product is 1197. We want to find $c$. 3. **Set up the equation:** $$3 \times 19 \times c = 1197.$$ 4. **Simplify the known product:** Calculate $3 \times 19$: $$3 \times 19 = 57.$$ 5. **Rewrite the equation:** $$57 \times c = 1197.$$ 6. **Solve for $c$:** Divide both sides by 57: $$c = \frac{1197}{57}.$$ 7. **Calculate the division:** $$c = 21.$$ **Answer:** The third number is **21**.