What is the optimal time complexity of solving Highest Common Factor(HCF)?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Highest Common Factor(HCF)?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Highest Common Factor(HCF)?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Highest Common Factor(HCF)?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Python BasicsEasy

Highest Common Factor(HCF)

Learn how to solve the 'Highest Common Factor(HCF)' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

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.

Constraints

•1 <= a, b <= 10^6

Examples

Example 1

Input

find_hcf(12, 18)

Output

Explanation

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.

Example 2

Input

find_hcf(24, 36)

Output

Explanation

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.

Example 3

Input

find_hcf(7, 13)

Output

Explanation

7 and 13 are both prime numbers with no common factors other than 1.

Need a Hint?

Use simple arithmetic operators (like modulo `%`, division `//`), conditional checks, or loops to inspect number properties.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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