How do we find greatest common divisor of 24 and 6?

Question

How do we find that $GCD(24,6) = 6$ ?

When i tried to use the "Euclidean algorithm" I got

$24 = 6*4 + 0$

Answer 1

Write all divisors for $$24:\;\;\; 1,2,3,4,6,8,12,24$$ and for $$6:\;\;\; 1,2,3,6$$ Which common divisor is the greatest?

Answer 2

When you use the Euclidean algorithm, the $\gcd$ is read of from the last divisor used (the one that gave a remainder of zero). You went one step too far and used the last remainder instead. In this case, the last divisor used was the only divisor ever used, namely $6$.

Answer 3

GCD of two numbers is the greatest number that is a divisor of both the numbers. So to find GCD we can proceed as Split the number in terms of prime factors. Pick out the factors that are common in both and multiply them to get GCD As $$ 24 = 1×2×2×2×3 = 1× 2^3×3 $$ $$ 6 = 1×2×3 $$ Thus the common factors are $ 1, 2 and 3 $. So GCD of the number is product of these factors So $$ GCD = 1×2×3 $$ $$ GCD = 6 $$