Teaching Kids Programming – Number of Common Factors (Brute Force Algorithm + Greatest Common Divisor)

Teaching Kids Programming: Videos on Data Structures and Algorithms

Given two positive integers a and b, return the number of common factors of a and b.

An integer x is a common factor of a and b if x divides both a and b.

Example 1:
Input: a = 12, b = 6
Output: 4
Explanation: The common factors of 12 and 6 are 1, 2, 3, 6.

Example 2:
Input: a = 25, b = 30
Output: 2
Explanation: The common factors of 25 and 30 are 1, 5.

Constraints:
1 <= a, b <= 1000

Number of Common Factors (Bruteforce Algorithm + Greatest Common Divisor)

We can bruteforce the numbers from 2 (inclusive) to the GCD (Greatest Common Divisor) between two numbers.

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class Solution:
    def commonFactors(self, a: int, b: int) -> int:
        x = gcd(a, b)
        ans = 1
        for i in range(2, x + 1):
            if x % i == 0:
                ans += 1
        return ans

class Solution:
    def commonFactors(self, a: int, b: int) -> int:
        x = gcd(a, b)
        ans = 1
        for i in range(2, x + 1):
            if x % i == 0:
                ans += 1
        return ans

And this can be written using one-liner:

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return sum(1 for i in range(1, x + 1) if x % i == 0)

return sum(1 for i in range(1, x + 1) if x % i == 0)

The GCD Algorithm (Teaching Kids Programming – Algorithms of Greatest Common Divisor and Least Common Multiples) of two integers:

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

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

And it can be done Recursively:

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def gcd(a, b):
  if b:
    return gcd(b, a % b)
  return a

def gcd(a, b):
  if b:
    return gcd(b, a % b)
  return a

The time complexity of GCD algorithm is

–EOF (The Ultimate Computing & Technology Blog) —

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