Calculating the factorial of a number using a recursive CTE in SQL can be both an instructive and practical example. Here’s a detailed step-by-step guide to achieve this.

### Step-by-Step Explanation

**Anchor Member**: The base case of the recursion. For the factorial calculation, the base case is`0! = 1`

or`1! = 1`

.**Recursive Member**: Defines the recursive step. For the factorial of`n`

, we have`n! = n * (n-1)!`

.

Here's the SQL code to calculate the factorial of a number (let's say `5`

):

### SQL Code

sql`WITH RECURSIVE FactorialCTE AS ( -- Anchor member: start with 1 SELECT 1 AS n, 1 AS factorial UNION ALL -- Recursive member: calculate factorial for n + 1 SELECT n + 1, factorial * (n + 1) FROM FactorialCTE WHERE n < 5 --Set the Dynamic limit to the desired number, in this case, 5 ) SELECT n, factorial FROM FactorialCTE ORDER BY n;`

### Explanation

**Anchor Member**:sql`SELECT 1 AS n, 1 AS factorial`

This initializes the recursion with

.**1! = 1****Recursive Member**:sql`SELECT n + 1, factorial * (n + 1) FROM FactorialCTE WHERE n < 5`

This part of the CTE calculates the factorial by multiplying the current value of

`factorial`

by

until**n + 1**`n`

reaches`5`

.**Final Select**:sql`SELECT n, factorial FROM FactorialCTE ORDER BY n;`

This selects and orders the results by

.**n**

### Result

The result will be a table listing each `n`

from `1`

to `5`

and the corresponding factorial value:

` n | factorial````
---|-----------
1 | 1
2 | 2
3 | 6
4 | 24
5 | 120
```

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