In the previous article, we have discussed Python Program for Modular Multiplicative Inverse

Given two numbers N and K, the task is to find the sum of Modulo K of the first N natural numbers in Python.

**Examples:**

**Example1:**

**Input:**

Given Number = 5 Given k value = 6

**Output:**

The sum of modulo k of the given n natural numbers = 15

**Explanation:**

here 1%6+2%6+3%6+4%6+5%6 gives 15

- Python Program for Given Two Numbers a and b Find all x Such that a % x = b
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- Python Program to Print Series 6, 9, 14, 21, 30, 41, 54 … N

**Example2:**

**Input:**

Given Number = 4 Given k value = 7

**Output:**

The sum of modulo k of the given n natural numbers = 10

## Program to Find Sum of Modulo K of First N Natural Numbers in Python

Below are the ways to find the sum of Modulo K of the first N natural numbers in Python.

### Method #1: Using For Loop (Static Input)

**Approach:**

- Give the number as static input and store it in a variable.
- Give the k value as static input and store it in another variable.
- Pass the given number and k value as the arguments to the
**Sum_mod_k**function. - Create a function to say
**Sum_mod_k**which takes the given number and k value as the arguments and returns the sum of modulo K of the given first N natural numbers. - Take a variable to say
**rslt**and initialize its value to 0. - Loop from 1 to the given number using the for loop.
- Calculate the value of the iterator modulus given k value and store it in a variable.
- Add the above result to the
**rslt**and store it in the same variable**rslt.** - Return the value of
**rslt.** - Print the sum of modulo K of the given first N natural numbers.
- The Exit of the Program.

**Below is the implementation:**

# Create a function to say Sum_mod_k which takes the given number and k value as the # arguments and returns the sum of modulo K of the given first N natural numbers. def Sum_mod_k(gvn_numb, gvn_Kval): # Take a variable to say rslt and initialize its value to 0. rslt = 0 # Loop from 1 to the given number using the for loop. for itr in range(1, gvn_numb + 1): # Calculate the value of the iterator modulus given k value and store it in a variable. mod_rslt = (itr % gvn_Kval) # Add the above result to the rslt and store it in the same variable rslt. rslt += mod_rslt # Return the value of rslt. return rslt # Give the number as static input and store it in a variable. gvn_numb = 5 # Give the k value as static input and store it in another variable. gvn_Kval = 6 # Pass the given number and k value as the arguments to the Sum_mod_k function. # Print the sum of modulo K of the given first N natural numbers. print("The sum of modulo k of the given n natural numbers = ", Sum_mod_k(gvn_numb, gvn_Kval))

**Output:**

The sum of modulo k of the given n natural numbers = 15

### Method #2: Using For loop (User Input)

**Approach:**

- Give the number as user input using the int(input()) function and store it in a variable.
- Give the k value as user input using the int(input()) function and store it in another variable.
- Pass the given number and k value as the arguments to the
**Sum_mod_k**function. - Create a function to say
**Sum_mod_k**which takes the given number and k value as the arguments and returns the sum of modulo K of the given first N natural numbers. - Take a variable to say
**rslt**and initialize its value to 0. - Loop from 1 to the given number using the for loop.
- Calculate the value of the iterator modulus given k value and store it in a variable.
- Add the above result to the
**rslt**and store it in the same variable**rslt.** - Return the value of
**rslt.** - Print the sum of modulo K of the given first N natural numbers.
- The Exit of the Program.

**Below is the implementation:**

# Create a function to say Sum_mod_k which takes the given number and k value as the # arguments and returns the sum of modulo K of the given first N natural numbers. def Sum_mod_k(gvn_numb, gvn_Kval): # Take a variable to say rslt and initialize its value to 0. rslt = 0 # Loop from 1 to the given number using the for loop. for itr in range(1, gvn_numb + 1): # Calculate the value of the iterator modulus given k value and store it in a variable. mod_rslt = (itr % gvn_Kval) # Add the above result to the rslt and store it in the same variable rslt. rslt += mod_rslt # Return the value of rslt. return rslt # Give the number as user input using the int(input()) function and store it in a variable. gvn_numb = int(input("Enter some random number = ")) # Give the k value as user input using the int(input()) function and store it in another variable. gvn_Kval = int(input("Enter some random number = ")) # Pass the given number and k value as the arguments to the Sum_mod_k function. # Print the sum of modulo K of the given first N natural numbers. print("The sum of modulo k of the given n natural numbers = ", Sum_mod_k(gvn_numb, gvn_Kval))

**Output:**

Enter some random number = 4 Enter some random number = 7 The sum of modulo k of the given n natural numbers = 10

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