7 Ways To Do Factorial In Microsoft Excel
Excel is just a really big and flexible calculator, so it makes sense that some people use it for math problems. The factorial comes up a lot in statistics when calculating permutations and combinations of events. So it’s likely one you’ll need to calculate quite a bit when doing any statistical work in Excel. This post will show you all the ways you can find the factorial of an integer number in Excel.
What is a Factorial?#
The factorial of an integer number is the product of all integers up to and including that number. The factorial of a number n is usually represented with an exclamation character n! after the number. Here are a few examples of factorial calculations.
5 factorial is represented as 5! and this is just 5 * 4 * 3 * 2 * 1 = 120.6 factorial is represented as 6! and this is just 6 * 5 * 4 * 3 * 2 * 1 = 720.7 factorial is represented as 7! and this is just 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040.
As you can see the values quickly get large. ⚠️ Warning: You will only be able to calculate up to 170! in Excel, and after this, the calculation will return a #NUM! error because the result will be too large.
Calculate the Factorial with the FACT Function#
Excel has a dedicated function for calculating the factorial of a number. The FACT function takes a positive integer value and returns the factorial for this number.
number is the number to return the factorial based on.
The above formula will return the factorial of the value in cell B3. The number passed to the FACT function needs to be a positive integer value.
Negative numbers will result in a #NUM! error.0 and 1 factorial will result in 1.Positive decimal values are truncated before the factorial is calculated.
Calculate the Factorial with the FACTDOUBLE Function#
There is another factorial function in Excel called FACTDOUBLE. From the function name, you might think it takes the factorial and multiplies it by 2. But this is not what it does. The double factorial (or semifactorial) is another mathematical calculation that is defined in a similar way to the factorial.
For even numbers, the double factorial is the product of all even integers up to and including that number.For odd numbers, the double factorial is the product of all odd integers up to and including that number.
The double factorial of n is represented by two exclamation mark characters n. Here are a few examples of double factorial calculations.
The double factorial of 5 is represented as 5!! and this is just 5 * 3 * 1 = 15.The double factorial of 6 is represented as 6!! and this is just 6 * 4 * 2 = 48.The double factorial of 7 is represented as 7!! and this is just 7 * 5 * 3 * 1 = 105.
This means the factorial of n is the same as the double factorial of n multiplied by the double factorial of n-1. In symbols this is n! = n!! * (n-1). The above formula will return the factorial of the value in cell B3. This formula calculates the double factorial of the number in cell B3 and the double factorial of the number in B3 minus 1, then multiplies the two double factorials which results in the factorial.
Calculate the Factorial with the SEQUENCE Function#
While there is a dedicated function to calculate your factorial values, there are some other creative options available. You can use a combination of the PRODUCT and SEQUENCE functions to create a factorial calculation. The above formula will return the factorial of the number in cell B3. The SEQUENCE function allows you to create a dynamic array of values that starts at 1 and increments by 1 up to the given number in cell B3. These are exactly the values you need to calculate a factorial. The PRODUCT function can then be used to multiply each of those values from the SEQUENCE. This result is exactly the factorial of the number in cell B3.
Calculate the Factorial with Power Query#
Power Query has many advanced mathematical functions available and this also includes a factorial function. You’ll be able to calculate the factorial for any column of numbers inside an Excel table using Power Query. This will open the Power Query editor where you will be able to add the factorial calculation to your data. This will apply something similar to the above M code formula as a step in your query and your column will now show the factorial values in the data preview. You can now load the data back into Excel. This will open the Import Data menu where you can select to import the data to a Table and then choose the location of the table.
Calculate the Factorial with the LAMBDA Function#
The factorial calculation is recursive. This means you can define the current value based on the previous value. The factorial of n is actually n multiplied by the factorial of n-1. In symbols this is n! = n * (n-1)!. There is one function in Excel that can handle recursive calculations. This is the LAMBDA function. The LAMBDA function allows you to build your own custom functions. You can use this to build your own version of a factorial function. To use the LAMBDA function recursively, you will first need to define your custom function with the name manager. This will open the Name Manager which lists all your named objects in the Excel workbook. �� Note: The Name used in the New Name menu must match what’s used in the Refers to input of the LAMBDA formula in order to recursively reference the calculations. The integer*FACTORIAL(integer-1) is the main part of the formula calculation which recursively calculates the factorial. The IF function tests the number first and applies the recursive calculation if it’s a number bigger than 1, otherwise, the factorial result will be 1. The LET function just helps to simplify the formula by defining integer as INT(n) which is the integer part of the number n. This is later used in multiple places in the factorial calculation. Alternatively, without the LET function, the LAMBDA formula could be written as above. The LET function will save the INT function from being used multiple times.
Now the new FACTORIAL function is defined in the Name Manager and it can be used just like any other function anywhere in the workbook. The above custom LAMBDA function will return the factorial based on the value in cell B3.
Calculate the Factorial with VBA#
VBA has a lot of built-in functions but there is no factorial function. But you can create a function that can be called in any other procedure to calculate the factorial if needed. The above code creates a factorial function that takes a number as its argument and returns the factorial. This code is a recursive definition as you can see the Factorial() function calls itself to perform the calculation.
Calculate the Factorial with Office Scripts#
The TypeScript based language found in Office Scripts also does not have a built-in factorial function available. But you can also build your own factorial calculation in a recursive manner which can then be called from your main function. The above Office Script function will return the factorial of a given number. The function is defined recursively. You can see that factorial() calls itself in the calculation.
Conclusions#
There are many reasons why you might need to calculate the factorial of a number in Excel. This post has shown you the different methods you can use. The most straightforward way to get the factorial will be with the FACT function. But alternatively, you can get the same result with a few other creative formulas involving the FACTDOUBLE, SEQUENCE, and PRODUCT functions. Power Query also offers a factorial M code formula that is easily used from the editor ribbon. Since the factorial can be recursively defined, you can even create your own custom function using the LAMBDA function’s recursive powers. A similar recursion logic can be used to build VBA and Office Scripts functions to get the factorial as well. Did you know all these ways to get the factorial in Excel? Let me know in the comments!
How To Do Factorial in Excel
In Microsoft Excel, mathematical operations play a vital role in data analysis and manipulation. One such operation that finds significance in various fields is the calculation of factorials.
Factorial measures allow us to compute the product of a given number and all positive integers less than it. This article aims to provide a comprehensive guide on how to do factorial in Excel, including their calculation methods, practical applications, limitations, and advanced functions.
Understanding Factorial
Before delving into Excel’s factorial functions, let’s understand the concept of factorial itself. Factorial represents the product of a number and all the positive integers less than it. It is denoted by the exclamation mark (!). For example, 5! (read as “5 factorial”) is equal to 5 x 4 x 3 x 2 x 1, resulting in 120.
Factorials are often used in mathematical equations, probability calculations, permutations, and combinations. In Excel, you can utilize various methods to calculate factorials based on your specific requirements.
Factorial Calculation in Excel
Calculate the Factorial with the FACT Function
The factorial of a number can be easily calculated in Excel using the FACT function.
The FACT function takes a positive integer value as input and returns the factorial of that number. Here, “number” refers to the value for which you want to calculate the factorial.
By using the formula above, you can find the factorial value present in cell B3.
It is important to note that the number passed to the FACT function must be a positive integer. Negative numbers will result in a #NUM! error. Additionally, the factorial of 0 and 1 is always 1. If you input a positive decimal value, it will be truncated before the factorial calculation.
Calculate the Factorial with the FACTDOUBLE Function
To calculate the factorial using the FACTDOUBLE function, you can use the following formula:
= FACTDOUBLE(B3) * FACTDOUBLE(B3 – 1)
By applying this formula, you will obtain the factorial of the value present in cell B3.
Calculate the Factorial with the SEQUENCE Function
In addition to the dedicated factorial functions, you can utilize the PRODUCT and SEQUENCE functions to calculate factorials in different ways.
To calculate the factorial using this method, follow these steps:
Use the SEQUENCE function to generate a dynamic array of values starting from 1 and incrementing by 1 up to the specified number in cell B3. These generated values represent the numbers needed for the factorial calculation.
= PRODUCT(SEQUENCE(B3))
By applying the above formula, you can calculate the factorial of the number present in cell B3.
The SEQUENCE function helps generate the required values for factorial calculation, and the PRODUCT function then multiplies those values together, resulting in the factorial of the number in cell B3.
Applying Factorial to Practical Scenarios
Factorial calculations in Excel extend beyond basic formulas and the FACT function. You can utilize factorials to solve various real-world problems. For instance, calculating permutations and combinations, finding multinomial coefficients, or determining probabilities in statistical analysis.
Factorial Limitations and Considerations
While factorial calculations are powerful, there are certain limitations and considerations to keep in mind when working with them in Excel. Excel has a limit to the value it can handle, known as the factorial limit. Once you exceed this limit, Excel displays an error message.
Moreover, factorials grow at an exponential rate, leading to exceptionally large numbers for relatively small inputs. As a result, factorial calculations can quickly surpass the capacity of Excel’s number precision, resulting in rounded or inaccurate values.
Advanced Factorial Functions
Excel offers advanced factorial functions beyond basic factorial calculation. Let’s explore a few notable ones:
Permutations and Combinations
In addition to calculating factorials, Excel provides functions to compute permutations and combinations. These functions, such as PERMUT and COMBIN, allow you to determine the number of permutations and combinations of a given set of elements.
Multifactorial and Double Factorial
Multifactorial and double factorial functions are variations of the standard factorial. Multifactorial calculates the factorial considering increments other than one, while double factorial calculates the product of every other integer.
Factorial with Negative Numbers
Excel’s GAMMA function enables you to calculate factorials of negative numbers. It uses the gamma function, which extends the concept of factorial to non-integer values.
Practical Applications of Factorial in Excel
Factorial calculations find applications in various fields, showcasing their versatility. Here are a few practical scenarios where factorials prove beneficial in Excel:
Probability and Statistics
Factorial calculations are crucial in probability and statistics. They help determine outcomes, calculate probabilities, and solve permutation and combination problems in statistical analysis.
Mathematics and Engineering
In mathematics and engineering, factorials aid in solving problems related to permutations, combinations, and arrangements. They play a significant role in solving combinatorial problems and determining possibilities.
Business and Finance
Factorials find application in business and finance for scenarios like calculating the number of ways to arrange items, evaluating permutations of investment portfolios, and determining outcomes in decision-making processes.
Tips and Tricks for Factorial Calculations
To optimize your factorial calculations in Excel, consider the following tips and tricks:
Avoiding Errors
When working with large factorials, it’s essential to be cautious of exceeding Excel’s limitations. Use appropriate error-handling techniques to handle situations where the factorial exceeds Excel’s capabilities.
Using Factorial with Other Excel Functions
Factorial calculations can be combined with other Excel functions to enhance your analysis. For example, using factorials in combination with statistical functions can yield valuable insights.
Conclusion
Factorials are a fundamental mathematical concept used in various disciplines, and Excel provides several methods to calculate them. Whether you opt for basic formulas, the FACT function, or explore advanced factorial functions, Excel equips you with the tools to perform factorial calculations efficiently. Understanding factorials and their applications can significantly enhance your data analysis and problem-solving capabilities in Excel.
Как сделать факториал в экселе
Предположим, что у вас шесть колокольчиков с разными тонами и вы хотите найти количество уникальных последовательностей, в которых каждый колокольчик можно запускать один раз. В этом примере вычисляются факториал из шести. Как правило, с помощью факториала можно подсчитать количество способов у организовать группу отдельных элементов (также называемых перестроениями). Чтобы вычислить факториал числа, используйте функцию ФАКТЫ.
В этой статье описаны синтаксис формулы и использование функции ФАКТР в Microsoft Excel.
Описание
Возвращает факториал числа. Факториал числа — это значение, равное 1*2*3*…* число.
Синтаксис
Аргументы функции ФАКТР описаны ниже.
Число — обязательный аргумент. Неотрицательное число, для которого вычисляется факториал. Если число не является целым, оно усекается.
Пример
Скопируйте образец данных из следующей таблицы и вставьте их в ячейку A1 нового листа Excel. Чтобы отобразить результаты формул, выделите их и нажмите клавишу F2, а затем — клавишу ВВОД. При необходимости измените ширину столбцов, чтобы видеть все данные.
Как узнать факториал числа в excel
Предположим, что у вас шесть колоколов с разными тонами и вы хотите найти количество уникальных последовательностей, в которых каждый колокол может запускаться один раз. В этом примере вычисляются факториал из шести. В общем, с помощью факториала можно подсчитать количество способов у организовать группу отдельных элементов (перемитации). Чтобы вычислить факториал числа, используйте функцию ФАКТС.
В этой статье описаны синтаксис формулы и использование функции ФАКТР в Microsoft Excel.
Описание
Возвращает факториал числа. Факториал числа — это значение, равное 1*2*3*…* число.
Синтаксис
Аргументы функции ФАКТР описаны ниже.
Число — обязательный аргумент. Неотрицательное число, для которого вычисляется факториал. Если число не является целым, оно усекается.
Пример
Скопируйте образец данных из следующей таблицы и вставьте их в ячейку A1 нового листа Excel. Чтобы отобразить результаты формул, выделите их и нажмите клавишу F2, а затем — клавишу ВВОД. При необходимости измените ширину столбцов, чтобы видеть все данные.
Факториал в Excel
В этой статье я расскажу о факториале, его свойствах и о том, как вычислить его значение с помощью Excel. Мы проверим, как точно вычисляет значение факториала формула Стирлинга и разберем решение типовых задач с факториалами, а на закуску — несколько видеороликов (и конечно расчетный файл эксель). Удачи!
- Что такое факториал
- Расчет факториала в Excel
- Формулы и свойства факториала
- Примеры задач с факториалом
- Видео о факториале
- Полезные ссылки по комбинаторике
Что такое факториал?
Символ $n!$ называется факториалом и обозначает произведение всех целых чисел от $1$ до $n$. Факториал определен только для целых неотрицательных чисел.
$$n!=1\cdot 2\cdot 3 \cdot . \cdot (n-1) \cdot n$$
По определению, считают, что $0!=1, 1!=1$. Далее:
$$ 2!=1 \cdot 2 = 2,\\ 3!=1 \cdot 2 \cdot 3= 6,\\ 4!=1 \cdot 2 \cdot 3\cdot 4= 24,\\ 5!=1 \cdot 2 \cdot 3\cdot 4\cdot 5= 120,\\ . $$
Факториал растет невероятно быстро (недаром он обозначается восклицательным знаком!), существенно быстрее степенной $x^n$ или даже экспоненциальной функции $e^n$ (но медленее чем $e^$)
Факториал широко применяется в комбинаторике — он равен числу всех перестановок $n$-элементного множества, а также входит в формулы для числа сочетаний и размещений. Факториал встречается в математическом анализе (чаще при разложениях функции в степенные ряды), а также в функциональном анализе и теории чисел.
Формулы и свойства факториала
Рекуррентная формула для факториала:
Факториал связан с гамма-функцией по формуле: $n!= \Gamma(n+1)$. Фактически, гамма-функция — обобщение понятия факториала на все положительные вещственные функции.
Для любого натурального $n$ выполняется:
$$ (n!)^2 \ge n^n \ge n! \ge n. $$
Любопытная формула связывает факториал и производную степенной функции:
Формула Стирлинга
Для приближенного вычисления факториала применяют асимптотическую формулу Стирлинга:
Обычно для расчетов берут только главный член:
$$ n! \approx \sqrt <2\pi n>\left( \frac \right )^n. $$
Ниже вы увидите пример расчета факториала по обычной формуле и с помощью формулы Стирлинга, которая, как видно, дает вполне хорошее приближение (начиная с $n=9$ относительная погрешность уже меньше 1%).
Расчет факториала в Эксель
Для нахождения факториала в Excel нужно использовать специальную функцию =ФАКТР($n$) , где $n$ — число, факториал которого нужно найти.
Пример расчета и ввода формулы ниже на скриншоте, также вы можете скачать расчетный файл
Примеры задач с факториалом
Рассмотрим решение типовых задач.
Пример 1. На полке стоят 8 дисков. Сколькими способами их можно расставить между собой?
Решение. Требуется найти число всех перестановок 8 различных объектов, что вычисляется как раз как факториал:
$$N=8!=1 \cdot 2 \cdot 3\cdot 4\cdot 5\cdot 6\cdot 7\cdot 8=40320.$$
Пример 2. Вычислить
Пример 3. Упростить выражение
Пример 4. Упростить дробь, содержащую факториал:
Видео о факториале
Небольшое учебное видео про факториал — определение, свойства, как быстро растет, как вычислить в Excel по встроенной формуле и по приближенной формуле Стирлинга.