divmod() in Python and its application

The divmod() method in python takes two numbers and returns a pair of numbers consisting of their quotient and remainder. 

Syntax : 

divmod(x, y)
x and y : x is numerator and y is denominator
x and y must be non complex

Examples:  

Input : x = 9, y = 3
Output :(3, 0)

Input : x = 8, y = 3
Output :(2, 2)

Explanation: The divmod() method takes two parameters x and y, where x is treated as numerator and y is treated as the denominator. The method calculates both x // y and x % y and returns both the values. 

• If x and y are integers, the return value is

(x // y, x % y)

• If x or y is a float, the result is

(q, x % y), where q is the whole part of the quotient.

Output: 

(5, 4) =  (1, 1)
(10, 16) =  (0, 10)
(11, 11) =  (1, 0)
(15, 13) =  (1, 2)
(6.0, 5) =  (2.0, 2.0)
(3, 9.0) =  (0.0, 3.0)
(13.5, 6.2) =  (3.0, 0.0)
(1.6, 10.7) =  (5.0, 0.10000000000000009)

Errors And Exceptions 

1. If either of the arguments (say x and y), is a float, the result is (q, x%y). Here, q is the whole part of the quotient.
2. If the second argument is 0, it returns Zero Division Error
3. If the first argument is 0, it returns (0, 0)

Practical Application: Check if a number is prime or not using divmod() function.  

Examples: 

Input : n = 7
Output :Prime

Input : n = 15
Output :Not Prime

Algorithm 

1. Initialise a new variable, say x with the given integer and a variable counter to 0
2. Run a loop till the given integer becomes 0 and keep decrementing it.
3. Save the value returned by divmod(n, x) in two variables, say p and q
4. Check if q is 0, this will imply that n is perfectly divisible by x, and hence increment the counter value
5. Check if the counter value is greater than 2, if yes, the number is not prime, else it is prime

Output: 

Not Prime

More Applications: 

Example 1: 

Output: 

14

Example 2:

Output: 

231