1. **State the problem:** We need to find the greatest integer among 4 consecutive odd integers whose sum is 256.
2. **Define variables:** Let the smallest odd integer be $x$. Then the next three consecutive odd integers are $x+2$, $x+4$, and $x+6$.
3. **Set up the equation:** The sum of these four integers is given as:
$$x + (x+2) + (x+4) + (x+6) = 256$$
4. **Simplify the equation:**
$$4x + (2 + 4 + 6) = 256$$
$$4x + 12 = 256$$
5. **Solve for $x$:**
$$4x = 256 - 12$$
$$4x = 244$$
$$x = \frac{244}{4} = 61$$
6. **Find the greatest integer:** The greatest integer is $x + 6 = 61 + 6 = 67$.
**Final answer:** The greatest integer is $67$.
Consecutive Odd Integers
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.