How do you solve Number of Common Factors on LeetCode?

Number of Common Factors (LeetCode #2427) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(sqrt(n)) time complexity and O(1) space complexity. Key insight: Understanding GCD can simplify the problem significantly.

What is the brute force solution for Number of Common Factors?

The brute force approach for Number of Common Factors is Brute Force, with O(n) time complexity and O(1) space complexity. We will check every integer from 1 to the minimum of a and b to see if it divides both numbers. This is a straightforward way to find common factors. The optimal Optimal Solution approach improves this to O(sqrt(n)).

What algorithm or data structure is used to solve Number of Common Factors?

Number of Common Factors uses the following concepts: Math, Enumeration, Number Theory. The recommended patterns to study are: Math, Enumeration.

What are the interview tips for Number of Common Factors?

Always clarify the problem and constraints before jumping to code. Discuss the brute-force approach first to show your thought process. Mention edge cases and how your solution handles them.

What are common mistakes when solving Number of Common Factors?

Not considering the case where a and b are equal. Failing to check both divisors when a number is a perfect square.

#2427

Number of Common Factors

Easy

MathEnumerationNumber TheoryMathEnumeration

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n)	O(sqrt(n))
Space	O(1)	O(1)

💡

Intuition

Time O(sqrt(n))Space O(1)

Instead of checking every number, we can find the greatest common divisor (GCD) of a and b, and then count the factors of the GCD. This is more efficient.

⚙️

Algorithm

6 steps

1Step 1: Calculate the GCD of a and b.
2Step 2: Initialize a counter to zero.
3Step 3: Loop through all integers from 1 to the square root of the GCD.
4Step 4: For each integer, check if it divides the GCD.
5Step 5: If it does, increment the counter. If the division results in a different integer, increment the counter again.
6Step 6: Return the counter as the number of common factors.

solution.py11 lines

1import math
2
3def commonFactors(a, b):
4    gcd_ab = math.gcd(a, b)
5    count = 0
6    for i in range(1, int(gcd_ab**0.5) + 1):
7        if gcd_ab % i == 0:
8            count += 1
9            if i != gcd_ab // i:
10                count += 1
11    return count

ℹ

Complexity note: The time complexity is O(sqrt(n)) because we only check up to the square root of the GCD to find factors. The space complexity is O(1) since we only use a few variables.

1Understanding GCD can simplify the problem significantly.
2Counting factors can be optimized by checking up to the square root.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.