# What are two consecutive odd positive integers whose product is 323?

Apr 11, 2018

$17$ and $19$.

#### Explanation:

$17$ and $19$ are odd, consecutive integers whose product is $323$.

Algebraic explanation:

Let $x$ be the first unknown. Then $x + 2$ must be the second unknown.

$x \cdot \left(x + 2\right) = 323 \text{ }$ Set up equation

${x}^{2} + 2 x = 323 \text{ }$ Distribute

${x}^{2} + 2 x - 323 = 0 \text{ }$ Set equal to zero

$\left(x - 17\right) \left(x - 19\right) = 0 \text{ }$ Zero product property

$x - 17 = 0 \mathmr{and} x - 19 = 0 \text{ }$ Solve each equation

$x = 17 \mathmr{and} x = 19$