# Find Three Consecutive Odd Integers Whose Sum is 63 by 3 Ways

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The sum of three consecutive odd integers is 63, what are these odd integers? I can easily tell you that the answer are 19, 21 and 23. You must be interested in how to find these 3 consecutive odd integers whose sum is 63. There are three methods here, let us introduce them one by one below.

## How to find three consecutive odd integers whose sum is 63?

### 1. Hypothetical method

Assuming that 2 * N + 1 is used to represent the first odd integer, so the second odd integer is 2 * N + 3, the third odd integer is 2 * N + 5.

Therefore, the sum of 3 consecutive odd integers is 63, which can be expressed by the equation

(2 * N + 1) + (2 * N + 3) + (2 * N + 5) = 63

Solve this equation

(2 * N + 1) + (2 * N + 3) + (2 * N + 5) = 63

2 * N + 1 + 2 * N + 3 + 2 * N + 5 = 63

6 * N + 1 + 3 + 5 = 63

6 * N + 9 = 63

6 * N = 63 – 9

6 * N = 54

N = 54 / 6

N = 9

So, 2 * N + 1 = 2 * 9 + 1 = 19

Now, we can get that 19 is the first integer of 3 consecutive odd integers whose sum is 63. So, the second odd integer is 21, the third odd integer is 23.

The answer came out, the sum of 3 consecutive odd integers is 63, these three odd integers are 19, 21 and 23.

Verify: 19 + 21 + 23 = 63. Correct!

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

### 2. Formula method

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

First(o) = S / M – M + 1

M represents the number of consecutive odd integers.

S stands for sum.

Back to the problem we want to solve: find three consecutive odd integers whose sum is 63. In here, M = 3, S = 63. Replace them in the formula to calculate the first odd integer

First(o) = 63 / 3 – 3 + 1 = 21 – 3 + 1 = 19

The first odd integer is 19, so, it can be easily calculated that the second odd integer is 21, the third odd integer is 23.

Thus, the answer are also 19, 21 and 23. Same as the first method. Then look at the third method, which is the simplest one.

### 3. Average method

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

The sum of 3 consecutive odd integers is 63, so, the average of these 3 consecutive odd integers is 63 / 3 = 21. The odd integers around 21 are 17, 18, 19, 20, 21, 22, 23, 24, 25. Now the problem is simple, find 3 consecutive odd integers from 17 to 25 and their average is 21. The answer are 19, 21 and 23.

So the sum of 3 consecutive odd integers is 63, these odd integers are 19, 21, 23. 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 odd integers whose sum is 63, some problems can be easily solved.

• 1. What are three consecutive odd integers whose sum is 63?
The answer are 19, 21 and 23.
• 2. What is the smallest of three consecutive odd integers whose sum is 63?
The smallest number is 19.
• 3. What is the middle of three consecutive odd integers whose sum is 63?
The middle integer is 21.
• 4. What is the greatest of three consecutive odd integers whose sum is 63?
The greatest number is 23.
• 5. What is the average of three consecutive odd integers whose sum is 63?
The average of these 3 consecutive odd integers is (19 + 21 + 23) / 3 = 63 / 3 = 21.
• 6. What is the product of three consecutive odd integers whose sum is 63?
The sum of 3 consecutive odd integers is 63, the product of them is 19 * 21 * 23 = 9177.
• 7. What is the sum of square of three consecutive odd integers whose sum is 63?
The sum of 3 consecutive odd integers is 63, the sum of their squares is 192 + 212 + 232 = 1331.

## Summarize

On this page, In addition to introducing three methods how to find three consecutive odd integers whose sum is 63, it also provides a calculator that calculates three consecutive odd 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 integers or consecutive 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 odd integers whose sum is 63. Personally, I prefer the second method, 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?