1Cademy - Solving for Two Consecutive Odd Integers Whose Product is $$323$$

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Problem-Solving Strategy for Word Problems

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Solving for Two Consecutive Odd Integers Whose Product is $323$

Apply the problem-solving strategy to find two consecutive odd integers whose product is $323$ .

Identify and Name: Let $n$ represent the first odd integer. The next consecutive odd integer is $n + 2$ .
Translate: The product of the two consecutive odd integers is $323$ , which translates to the equation $n(n + 2) = 323$ .
Solve: Distribute $n$ to get $n^2 + 2n = 323$ . Bring all terms to one side to write the quadratic equation in standard form: $n^2 + 2n - 323 = 0$ . Factor the trinomial to obtain $(n - 17)(n + 19) = 0$ . Using the Zero Product Property, solve to find $n = 17$ or $n = -19$ .

There are two sets of solutions:

If the first integer is $17$ , the next consecutive odd integer is $17 + 2 = 19$ .
If the first integer is $-19$ , the next consecutive odd integer is $-19 + 2 = -17$ .

Check: $17 \cdot 19 = 323$ and $-19(-17) = 323$ . Both pairs are valid solutions.
Answer: The consecutive odd integers are $17$ and $19$ , and $-19$ and $-17$ .

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Updated 2026-05-25

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