# Find Three Consecutive Integers Whose Sum is 108 by 3 Ways

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The sum of three consecutive integers is 108, what the integers? I can easily tell you that the answer are 35, 36 and 37. You must be interested in how to find these 3 consecutive integers whose sum is 108. There are three methods here, let us introduce them one by one below.

## 1. Find three consecutive integers whose sum is 108 by hypothetical method

Assuming that **N** is used to represent the first integer, so the second integer is N + 1, the third integer is N + 2.

Therefore, the sum of 3 consecutive integers is 108, which can be expressed by the equation

N + (N + 1) + (N + 2) = 108

Solve this equation

N + (N + 1) + (N + 2) = 108

N + N + 1 + N + 2 = 108

3 * N + 1 + 2 = 108

3 * N + 3 = 108

3 * N = 108 – 3

3 * N = 105

N = 105 / 3

N = 35

Now, we can get that 35 is the first integer of 3 consecutive integers whose sum is 108. So, the second integer is 36, the third integer is 37.

The answer came out, the sum of 3 consecutive integers is 108, these three integers are 35, 36 and 37.

Verify: 35 + 36 + 37 = 108. Correct!

This is the most common method, let’s look at the second method, which is my favorite method.

## 2. Find three consecutive integers whose sum is 108 by formula method

According to the consecutive integers calculator based on sum, we can know that the sum of **M** consecutive integers is **S**, the first integer formula is

First(n) = S / M – (M – 1) / 2

**M represents the number of consecutive integers.**

**S stands for sum.**

Back to the problem we want to solve: find three consecutive integers whose sum is 108. In here, **M = 3, S = 108**. Replace them in the formula to calculate the first integer

First(n) = 108 / 3 – (3 – 1) / 2 = 36 – (3 – 1) / 2 = 36 – 1 =35

The first integer is 35, so, it can be easily calculated that the second integer is 36, the third integer is 37.

Thus, the answer are also 35, 36 and 37. Same as the first method. Then look at the third method, which is the simplest one.

## 3. Find three consecutive integers whose sum is 108 by average method

The principle is very simple, because we want to calculate the consecutive integers, so after calculating the average, we can find the integers near the average.

The sum of 3 consecutive integers is 108, so, the average of these 3 consecutive integers is **108 / 3 = 36**. The integers around 36 are 34, 35, 36, 37, 38, 39. Now the problem is simple, find 3 consecutive integers from 34 to 39 and their average is 36. The answer are 35, 36 and 37.

So the sum of 3 consecutive integers is 108, these integers are 35, 36, 37. The results are consistent with the above two methods. Is it very simple?

## Problems can be sloved by this answer

Now, we have found out these 3 consecutive integers whose sum is 108, some problems can be easily solved.

- The sum of three consecutive integers is 108, the smallest one is 35.
- The sum of three consecutive integers is 108, the middle integer is 36.
- 37 is the greatest number of three consecutive integers whose sum is 108.
- The sum of three consecutive integers is 108, the product of them is 35 * 36 * 37 = 46620.
- The sum of three consecutive integers is 108, the average of these integers is 36.
- The sum of three consecutive integers is 108, the sum of their squares is 35
^{2}+ 36^{2}+ 37^{2}= 3890.

## Summarize

On this page, In addition to introducing three methods how to find three consecutive integers whose sum is 108, it also provides a calculator that calculates three consecutive integers based on the sum. If you encounter a similar problem next time, you can directly use this calculator to calculate the answer, which is very convenient.

Of course, if the problem you encounter is more complicated, such as: the number of consecutive integers is not 3, or you need to calculate consecutive odd integers or even integers. You can use our other more advanced sum-based consecutive integers calculator, where you can specify the number of consecutive integers and select consecutive integers type: natural integers, odd integers or even integers. I believe it can help you.

Well, that’s it, the above are three solutions to find three consecutive integers whose sum is 108. It’s not very complicated, but I personally like the second method best, because it can accurately calculate the first integer and the calculation process is very simple. So how about you? Please leave a message and tell me which method you like?