# Product of Consecutive Integers Calculator

Product result:

## Related calculator

In addition to the sum of consecutive integers, we are often asked to calculate the product of consecutive integers. Compared with the sum of consecutive integers, it is more difficult to calculate the consecutive integers product manually. Therefore, it is very necessary to provide a consecutive integers product calculator, which allows you to easily complete the product of consecutive integers.

Similar to the sum of consecutive integers calculator, the product calculator can not only calculate consecutive integers product, but also calculate the product of consecutive odd integers or even integers separately.

## Consecutive integers product formula

Let’s first look at a simple example, the product of consecutive numbers from 1 to 5, the answer is

1 * 2 * 3 * 4 * 5.

Are you familiar with this calculation? Yes, it is the factorial in mathematics

5! = 5 * 4 * 3 *  2 * 1

The order is reversed but the calculated results are consistent. Thus, if we find the consecutive integers product from 1 to N, it can be calculated by factorial.

But if the starting number is not 1, as in the example above, if the starting number is 3, calculate consecutive integers product from 3 to 5. How to calculate? It’s simple: 3 * 4 * 5. But if there are many consecutive integers, such as the product of consecutive integers from 3 to 100, it is obviously impossible to list them one by one. Is there a general formula to express it? Let’s look at the product of continuous integers from 3 to 5. If we multiply expression by 1 * 2, it is the factorial of 5, but the factorial of 5 is not the result we want. The result we want must be excluded 1 * 2, so the equation can be converted to

3 * 4 * 5 = 1 * 2 * 3 * 4 * 5 / 1 * 2 = 5! / 2!

Now, let’s sort it out, if the starting number is A and the ending number is B, then the formula of consecutive integers product is:

Product(A, B) = B! / (A – 1)!

To verify, we calculate an example: find the consecutive integers product from 6 to 10.

The first method, list all integers directly, and then multiply them

6 * 7 * 8 * 9  * 10 = 30240

The second method, using the formula above, A = 6, B = 10, so the expression is:

10! / (6 – 1)! = 3628800 / 120 = 30240

Obviously, the result calculated by the formula is consistent with the first approach. So this consecutive integers product formula meets our requirements.

## How to use product of consecutive integers calculator

Here, we are going to introduce the steps to use the consecutive integers product calculator. It’s very simple, just 4 steps.

##### Step 1

Enter the starting integer.

##### Step 2

Enter the ending integer.

##### Step 3

Select the type, consecutive integers, consecutive even integers or consecutive odd integers, the default is consecutive integers.

##### Step 4

Click the calculation button. ## Product of consecutive integers examples

Now, introduce some examples, so that you can more clearly understand how to use the consecutive integers product calculator.

Example 1: the product of consecutive integers between 15 to 20

Enter the number 15 in the first box and number 20 in the second box, then click calculation button. Example 2: the product of consecutive even integers from 10 to 20

First, enter the number 10 into the first input box, then enter 20 into the second input box. Third, select the even integers type. Fourth, click calculate button. Example 3: consecutive odd integers product from 10 to 20

Similar to the second example, but select the odd integers type in the third step. • 1. Can I input a negative number?

Yes, of course.

• 2. Does the calculation of consecutive integers include decimals?

Excluding decimals, this is used to calculate the product of consecutive integers, without decimals in the calculation process.

• 3. Is there a general formula for the product of consecutive even integers or consecutive odd integers?

Yes, There are have general formulas, but these formulas are relatively complicated and not very practical, so the article does not discuss them in detail. Of course, if you are interested, please leave a message to us and we can discuss them in depth.

• 4. Does the calculated result contain only positive integers?

Of course not, it also contains negative integers, if the conditions are met.

## Conclusion

Compared with the sum of consecutive integers, the product of consecutive integers is much more complicated, especially for the product of consecutive even or odd integers. If there is no consecutive integers product calculator, the desired result must be obtained through multiple calculations. So the consecutive integers product calculator should be very practical for you. Just enter the starting number and ending number, the result will show immediately. Of course, if you have any questions or difficulties during use, you can leave us a message, and we will reply as soon as possible, thank you!