Exercise 454Number theory › Divisibility and gcdHigh schoolAdded 3 Nov 2026

GCD of three numbers

#gcd#three numbers#Euclidean

Statement

Compute $\gcd(120, 84, 36)$ .

Hint

Compute $\gcd(120,84)$ first, then $\gcd$ of the result with $36$ .

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Euclidean. $\gcd(120,84)$ : $120=1\cdot84+36$ , $84=2\cdot36+12$ , $36=3\cdot12+0$ . So $\gcd(120,84)=12$ .

Then. $\gcd(12,36)=12$ .

Conclusion. $\gcd(120,84,36)=12$ .

Remark. The GCD of several numbers can be computed by taking GCDs pairwise.