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

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

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

Practice Python Program Examples to master coding skills and learn the fundamental concepts in the dynamic programming language Python.