3 Greatest Common Divisor GCD
Problem Statement
Write recursive code to calculate the Greatest Common Divisor (GCD) of Two Positive Numbers.
The greatest common divisor (GCD) of two positive integers A and B is the largest positive integer that divides both A and B without leaving a remainder.
Let's see some example inputs/outputs for this example:
| Input(s) | Output(s) | Explanation |
|---|---|---|
| A = 12, B = 18 | GCD = 6 | The factors of 12 are [1, 2, 3, 4, 6, 12], and the factors of 18 are [1, 2, 3, 6, 9, 18]. The common factors between 12 and 18 are [1, 2, 3, 6], and the largest common factor is 6. |
| A = 25, B = 15 | GCD = 5 | The factors of 25 are [1, 5, 25], and the factors of 15 are [1, 3, 5, 15]. The common factors between 25 and 15 are [1, 5], and the largest common factor is 5. |
| A = 40, B = 60 | GCD = 20 | The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40], and the factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. The common factors between 40 and 60 are [1, 2, 4, 5, 10, 20], and the largest common factor is 20. |
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Code
Here is the code for this algorithm:
🎯 STRICT STANDOUT — Problem cue: GCD (Euclid)
1. Why
Euclid gcd(a,b)=gcd(b,a%b), base b=0→a. Logarithmic depth — remainders shrink fast.
2. Big-O (K11)
Worst Fibonacci pair: O(log_φ a) steps still O(log a); stack O(log a)
Subtraction Euclid can be Θ(a) — avoid3. Pattern + when-NOT
EUCLIDEAN RECURSION. When-NOT: subtraction form; binary GCD for bit ops sometimes.
4. Edge
gcd(48,18)=6; gcd(7,0)=7; gcd(0,0) specify; gcd(1,1)=15. Panel
Q: Why not O(n)? A: Modulo shrinks exponentially, not by 1.
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