# The product of two consecutive integers is 56. How do you find the integers?

Jun 2, 2016

The two numbers are 7 and 8.

#### Explanation:

$\textcolor{b l u e}{\text{From the multiplications tables}}$

$\textcolor{g r e e n}{7 \times 8 = 56}$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{The algebra way}}$
Let the first number be $n$

Then the second number is $n + 1$

The product is $n \times \left(n + 1\right) = 56$

$\implies {n}^{2} + n - 56 = 0$

Known: $7 \times 8 = 56$. However the equation's 56 is nagetive, so one of the 7 and 8 is negative.
The equation has $+ n$ so the larger of the two is positive. Giving:

$\left(n - 7\right) \left(n + 8\right) = 0$

$\implies n = + 7 \text{ and } n = - 8$

As a first number $n = - 8$ is not logical so the first number is $n = 7$

Thus the second number is 8.