Question

Write a function greatest_common_divisor that takes two inputs a

and b and returns the greatest common divisor of the two numbers.
E.g. input (10, 15) would return 5

Answer 1

The function greatest_common_divisor calculates the Greatest Common Divisor (GCD) of two numbers, which is the highest number that divides both without any remainder. The GCD for the input (10, 15) is 5.

Step-by-step explanation:

The function greatest_common_divisor is used to find the highest number that divides both of the given numbers without any remainder. In Mathematics, this is known as the Greatest Common Divisor (GCD), sometimes referred to as the greatest common factor or highest common factor. A commonly used method to find the GCD of two numbers is the Euclidean algorithm.

A simple implementation in Python could look like this:

def greatest_common_divisor(a, b):
while b:
a, b = b, a % b
return a

When greatest_common_divisor is called with the inputs (10, 15), it will return 5, because 5 is the largest number that can exactly divide both 10 and 15.

The greatest common divisor (GCD) of two numbers is the largest positive integer that divides both numbers without leaving a remainder. To find the GCD of two numbers, a and b, you can use the Euclidean algorithm. Here's an example:

Start with the two numbers, a = 10 and b = 15.

Divide the larger number (15) by the smaller number (10): 15 ÷ 10 = 1 with a remainder of 5.

Replace the larger number (15) with the remainder (5).

Repeat the process until the remainder is 0. In this case, 5 ÷ 1 = 5 with a remainder of 0.

The last non-zero remainder (5) is the GCD of the two numbers, 10 and 15.

In this case, the GCD of 10 and 15 is 5.