Highest Common Factor(HCF)
Detailed guide and Python implementation for the 'Highest Common Factor(HCF)' problem.
1. Concept Overview
The 'Highest Common Factor(HCF)' problem is a key challenge in the Numbers section.
This implementation focuses on easy-level logic in Python.
We prioritize technical accuracy and code readability in our provided solutions.
2. Real-World Applications
3. Visual Intuition
Visualizing the logic flow for Highest Common Factor(HCF).
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for Highest Common Factor(HCF) carefully.
2. Formulate brute force
Draft a simple iterative solution.
3. Identify inefficiency
Look for redundant calculations.
4. Optimize search path
Use hashing or sorting to speed up the process.
5. Final Implementation
Clean up the code for production standards.
Problem Statement
Write a function find_hcf(a, b) that takes two positive integers a and b and returns their Highest Common Factor (HCF). The HCF is the largest positive integer that divides both numbers without leaving a remainder.
For example, the HCF of 12 and 18 is 6, because 6 is the largest number that divides both 12 and 18 evenly.
- •1 <= a, b <= 10^6
Examples
find_hcf(12, 18)
6
Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. Common factors: 1, 2, 3, 6. Highest is 6.
find_hcf(24, 36)
12
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Highest common factor is 12.
find_hcf(7, 13)
1
7 and 13 are both prime numbers with no common factors other than 1.
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
Ready to Solve?
Open the problem in PyRun's browser-based Python editor. Your code runs fully offline — no server required.
Interview Insights & Variations
Complexity Analysis Breakdown
Why Time: Directly evaluates all possibilities.
Why Space: Uses standard local memory.
Why Time: Optimized paths reduce total operations.
Why Space: May trade memory for speed.
Optimized Solution Python Code
Optimized Solution Python Code
def hcf_opt(a, b):
while b:
a, b = b, a % b
return aBrute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def hcf_brute(a, b):
hcf = 1
for i in range(1, min(a, b) + 1):
if a % i == 0 and b % i == 0:
hcf = i
return hcfAlgorithm Pattern Checklist
When dealing with Numbers data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
Related Questions
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