﻿ Python Math: Implement Euclidean Algorithm to compute the greatest common divisor - w3resource # Python Math: Implement Euclidean Algorithm to compute the greatest common divisor

## Python Math: Exercise-76 with Solution

Write a Python program to implement Euclidean Algorithm to compute the greatest common divisor (gcd).

Note: In mathematics, the Euclidean algorithm[a], or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two numbers, the largest number that divides both of them without leaving a remainder.

The Euclidean algorithm is based on the principle that the greatest common divisor of two numbers does not change if the larger number is replaced by its difference with the smaller number. For example, 21 is the GCD of 252 and 105 (252 = 21 × 12 and 105 = 21 × 5), and the same number 21 is also the GCD of 105 and 147 = 252 − 105.

Sample Solution:-

Python Code:

``````from math import *

def euclid_algo(x, y, verbose=True):
if x < y: # We want x >= y
return euclid_algo(y, x, verbose)
print()
while y != 0:
if verbose: print('%s = %s * %s + %s' % (x, floor(x/y), y, x % y))
(x, y) = (y, x % y)

if verbose: print('gcd is %s' % x)
return x

euclid_algo(150, 304)
euclid_algo(1000, 10)
euclid_algo(150, 9)
```
```

Sample Output:

```304 = 2 * 150 + 4
150 = 37 * 4 + 2
4 = 2 * 2 + 0
gcd is 2

1000 = 100 * 10 + 0
gcd is 10

150 = 16 * 9 + 6
9 = 1 * 6 + 3
6 = 2 * 3 + 0
gcd is 3
```

Pictorial Presentation: Flowchart: ## Visualize Python code execution:

The following tool visualize what the computer is doing step-by-step as it executes the said program:

Python Code Editor:

Have another way to solve this solution? Contribute your code (and comments) through Disqus.

What is the difficulty level of this exercise?

Test your Python skills with w3resource's quiz

﻿

## Python: Tips of the Day

Python: Get the Key Whose Value Is Maximal in a Dictionary

```>>> model_scores = {'model_a': 100, 'model_z': 198, 'model_t': 150}
>>> # workaround
>>> keys, values = list(model_scores.keys()), list(model_scores.values())
>>> keys[values.index(max(values))]
'model_z'
>>> # one-line
>>> max(model_scores, key=model_scores.get)
'model_z'
```