# Find Six Consecutive Integers Whose Sum is 393 by 3 Ways

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The sum of six consecutive integers is 393, what the integers? I can easily tell you that the answer are 63, 64, 65, 66, 67 and 68. You must be interested in how to find these 6 consecutive integers whose sum is 393. There are three methods here, let us introduce them one by one below.

## 1. Find six consecutive integers whose sum is 393 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, the 4th integer is N + 3, the 5th integer is N + 4, the 6th integer is N + 5.

Therefore, the sum of 6 consecutive integers is 393, which can be expressed by the equation

N + (N + 1) + (N + 2) + (N + 3) + (N + 4) + (N + 5) = 393

Solve this equation

N + (N + 1) + (N + 2) + (N + 3) + (N + 4) + (N + 5) = 393

N + N + 1 + N + 2 + N + 3 + N + 4 + N + 5 = 393

6 * N + 1 + 2 + 3 + 4 + 5 = 393

6 * N + 15 = 393

6 * N = 393 – 15

6 * N = 378

N = 378 / 6

N = 63

Now, we can get that 63 is the first integer of 6 consecutive integers whose sum is 393. So, the second integer is 64, the third integer is 65, the 4th integer is 66, the 5th integer is 67, the 6th integer is 68.

The answer came out, the sum of 6 consecutive integers is 393, these three integers are 63, 64, 65, 66, 67 and 68.

Verify: 63 + 64 + 65 + 66 + 67 + 68 = 393. Correct!

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

## 2. Find six consecutive integers whose sum is 393 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 six consecutive integers whose sum is 393. In here, M = 6, S = 393. Replace them in the formula to calculate the first integer

First(n) = 393 / 6 – (6 – 1) / 2 = 65.5 – (6 – 1) / 2 = 65.5 – 5 / 2 = 65.5 – 2.5 = 63

The first integer is 63, so, it can be easily calculated that the second integer is 64, the third integer is 65, the 4th integer is 66, the 5th integer is 67, the 6th integer is 68.

Thus, the answer are also 63, 64, 65, 66, 67 and 68. Same as the first method. Then look at the third method, which is the simplest one.

## 3. Find six consecutive integers whose sum is 393 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 6 consecutive integers is 393, so, the average of these 6 consecutive integers is 393 / 6 = 65.5. The integers around 65.5 are 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72. Now the problem is simple, find 6 consecutive integers from 60 to 72 and their average is 65.5. The answer are 63, 64, 65, 66, 67 and 68.

So the sum of 6 consecutive integers is 393, these integers are 63, 64, 65, 66, 67, 68. 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 6 consecutive integers whose sum is 393, some problems can be easily solved.

• The sum of six consecutive integers is 393, the smallest one is 63.
• The sum of six consecutive integers is 393, the greatest integer is 68.
• The sum of six consecutive integers is 393, the average of these integers is 65.5.
• The sum of six consecutive integers is 393, the product of them is 63 * 64 * 65 * 66 * 67 * 68 = 1496996352.
• The sum of six consecutive integers is 393, the sum of their squares is 632 + 642 + 652 + 662 + 672 + 682 = 25759.

## Summarize

On this page, In addition to introducing three methods how to find six consecutive integers whose sum is 393, it also provides a calculator that calculates six 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 6, 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 six consecutive integers whose sum is 393. 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?