Exercise 548Number theory › PrimesHigh schoolAdded 3 Nov 2026

Iterated GCD

#gcd#iteration#associativity

Statement

Compute $\gcd(24,36,60,84)$ .

Hint

Compute pairwise: $\gcd(24,36)=12$ , then $\gcd(12,60)=12$ , then $\gcd(12,84)=12$ .

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Iterate.
- $\gcd(24,36)=12$
- $\gcd(12,60)=12$
- $\gcd(12,84)=12$

Conclusion. $\gcd=12$ .

Prime factorization check. $24=2^3\cdot3$ , $36=2^2\cdot3^2$ , $60=2^2\cdot3\cdot5$ , $84=2^2\cdot3\cdot7$ . Common part: $2^2\cdot3=12$ . ✓