Python: Find common divisors between two numbers in a given pair

Last update on December 21 2024 07:19:19 (UTC/GMT +8 hours)

Common Divisors Finder

Write a Python program to find common divisors between two numbers in a given pair.

Visual Presentation:

Sample Solution:

Python Code:

# Function to calculate the greatest common divisor (GCD) of two numbers
def ngcd(x, y):
    i = 1
    while(i <= x and i <= y):
        # Check if both x and y are divisible by i
        if(x % i == 0 and y % i == 0):
            gcd = i  # Set gcd to the current common factor
        i += 1
    return gcd

# Function to calculate the number of common divisors of two numbers
def num_comm_div(x, y):
    # Calculate the greatest common divisor (GCD) using the ngcd function
    n = ngcd(x, y)
    result = 0
    z = int(n ** 0.5)  # Square root of n
    i = 1
    while(i <= z):
        if(n % i == 0):
            result += 2  # Increment the count for each pair of divisors
            if(i == n/i):
                result -= 1  # Adjust count if i is a perfect square divisor
        i += 1
    return result

# Test cases
print("Number of common divisors: ", num_comm_div(2, 4))
print("Number of common divisors: ", num_comm_div(2, 8))
print("Number of common divisors: ", num_comm_div(12, 24))

Sample Output:

Number of common divisors:  2
Number of common divisors:  2
Number of common divisors:  6

Explanation:

Here is the breakdown of the above Python exercise:

• User Input:
• tn = int(input("Input third term of the series:")): Takes user input for the third term of the arithmetic series.
• tltn = int(input("Input 3rd last term:")): Takes user input for the third-last term of the arithmetic series.
• s_sum = int(input("Sum of the series:")): Takes user input for the sum of the arithmetic series.
• Calculate Series Length:
• n = int(2 * s_sum / (tn + tltn)): Calculates the length of the arithmetic series using the sum formula.
• Calculate Common Difference:
• Determines the common difference 'd' based on the length of the series.
• If n - 5 == 0, it sets d = (s_sum - 3 * tn) // 6.
• Otherwise, it sets d = (tltn - tn) / (n - 5).
• Calculate First Term:
• a = tn - 2 * d: Calculates the first term 'a' of the arithmetic series using the third term and common difference.
• Print Series:
• Prints the arithmetic series using a loop and the calculated first term and common difference.

Flowchart:

Python Code Editor:

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