# How do you find two consecutive integers whose product is 783?

##### 2 Answers

See a solution process below:

#### Explanation:

First, let's call the first integer:

Then, the next consecutive integer would be by definition:

We can then write and solve this equation for find

We can now use the quadratic equation to solve this problem:

The quadratic formula states:

For

Substituting:

As show by this answer there are not two consecutive integers which when multiplied give 783.

There are however two consecutive **ODD** integers which when multiplied give 783:

Consecutive ODD numbers which give

#### Explanation:

At first glance we should see that there are no such integers....

Integers alternate between odd and even all the way along the number line. Therefore one of every two consecutive numbers will be even. The multiple of any even number is always even.

However, if the question is supposed to read

The product of two consecutive ODD numbers is

If the factors of a number, such as

The difference between any pairs of factors are greatest for the outer factors and smallest for the inner factors.

In the case of

Consecutive factors differ by

Consider

Factors are

In the case of

This is very close to

Check: