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

## Python Basic - 1: Exercise-29 with Solution

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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