Find Greatest Common Divisor of Array - Practice Coding Problems

Find Greatest Common Divisor of Array - Problem

Given an integer array nums, your task is to find the greatest common divisor (GCD) of the smallest and largest numbers in the array.

The greatest common divisor of two numbers is the largest positive integer that evenly divides both numbers without leaving a remainder.

Example: If we have the array [2, 5, 6, 9, 10], the smallest number is 2 and the largest is 10. The GCD of 2 and 10 is 2, since 2 is the largest number that divides both 2 and 10 evenly.

Goal: Return the GCD of the minimum and maximum values in the given array.

Input & Output

example_1.py — Basic Case

$ Input: [2, 5, 6, 9, 10]

› Output: 2

💡 Note: The smallest number is 2 and the largest is 10. GCD(2, 10) = 2 because 2 is the largest number that divides both 2 and 10 evenly.

example_2.py — Coprime Numbers

$ Input: [7, 5, 6, 8, 3]

› Output: 1

💡 Note: The smallest number is 3 and the largest is 8. GCD(3, 8) = 1 because 3 and 8 share no common factors other than 1.

example_3.py — Single Element

$ Input: [10]

› Output: 10

💡 Note: When there's only one element, both min and max are the same number (10), so GCD(10, 10) = 10.

Visualization

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Understanding the Visualization

Scan Array

Find the minimum and maximum values in one pass

Apply Euclidean Algorithm

Use the mathematical formula: GCD(a,b) = GCD(b, a mod b)

Return Result

When one number becomes 0, return the other as GCD

Key Takeaway

🎯 Key Insight: We only need the array's extreme values (min/max), then the Euclidean algorithm efficiently finds their GCD in logarithmic time!

Time & Space Complexity

Time Complexity

⏱️

O(n + log(min(a,b)))

O(n) to find min/max using built-in functions, O(log(min(a,b))) for Euclidean algorithm

⚡ Linearithmic

Space Complexity

O(1)

Only using constant extra space for variables

✓ Linear Space

Constraints

2 ≤ nums.length ≤ 1000
1 ≤ nums[i] ≤ 1000
All elements are positive integers

Asked in

G Google 15 a Amazon 12 ⊞ Microsoft 8 Apple 6

The optimal solution uses built-in min() and max() functions to find extreme values in O(n) time, then applies the Euclidean algorithm to calculate GCD in O(log(min)) time. Total complexity: O(n + log(min)) with O(1) space.

Common Approaches

Approach	Time	Space	Notes
✓ Optimal Solution (Built-in Functions)	O(n + log(min(a,b)))	O(1)	Use built-in min/max functions and Euclidean algorithm for GCD

Optimal Solution (Built-in Functions) — Algorithm Steps

Use built-in min() and max() functions to find extreme values in O(n)
Apply the Euclidean algorithm: GCD(a,b) = GCD(b, a mod b)
Repeat until one number becomes 0, return the other number
Alternative: use built-in GCD function if available

Visualization

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Step-by-Step Walkthrough

Quick Min/Max

Use built-in functions for O(n) min/max finding

Euclidean Algorithm

GCD(10,2) → GCD(2,0) → Result: 2

Return Result

Efficiently calculated GCD in O(log(min)) time

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>

int gcd(int a, int b) {
    while (b != 0) {
        int temp = b;
        b = a % b;
        a = temp;
    }
    return a;
}

int findGCD(int* nums, int n) {
    // Find min and max values
    int minVal = nums[0];
    int maxVal = nums[0];
    
    for (int i = 1; i < n; i++) {
        if (nums[i] < minVal) minVal = nums[i];
        if (nums[i] > maxVal) maxVal = nums[i];
    }
    
    // Use Euclidean algorithm for GCD
    return gcd(minVal, maxVal);
}

int main() {
    int n;
    scanf("%d", &n);
    int* nums = (int*)malloc(n * sizeof(int));
    for (int i = 0; i < n; i++) {
        scanf("%d", &nums[i]);
    }
    printf("%d\n", findGCD(nums, n));
    free(nums);
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n + log(min(a,b)))

O(n) to find min/max using built-in functions, O(log(min(a,b))) for Euclidean algorithm

⚡ Linearithmic

Space Complexity

O(1)

Only using constant extra space for variables

✓ Linear Space

Constraints

2 ≤ nums.length ≤ 1000
1 ≤ nums[i] ≤ 1000
All elements are positive integers

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Input & Output

Visualization

Time & Space Complexity

Related Problems

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Common Approaches

Optimal Solution (Built-in Functions) — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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