The GCD of given numbers is 1.
Step 1 :
Divide $ 334 $ by $ 233 $ and get the remainder
The remainder is positive ($ 101 > 0 $), so we will continue with division.
Step 2 :
Divide $ 233 $ by $ \color{blue}{ 101 } $ and get the remainder
The remainder is still positive ($ 31 > 0 $), so we will continue with division.
Step 3 :
Divide $ 101 $ by $ \color{blue}{ 31 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 4 :
Divide $ 31 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is still positive ($ 7 > 0 $), so we will continue with division.
Step 5 :
Divide $ 8 $ by $ \color{blue}{ 7 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 6 :
Divide $ 7 $ by $ \color{blue}{ 1 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.
We can summarize an algorithm into a following table.
334 | : | 233 | = | 1 | remainder ( 101 ) | ||||||||||
233 | : | 101 | = | 2 | remainder ( 31 ) | ||||||||||
101 | : | 31 | = | 3 | remainder ( 8 ) | ||||||||||
31 | : | 8 | = | 3 | remainder ( 7 ) | ||||||||||
8 | : | 7 | = | 1 | remainder ( 1 ) | ||||||||||
7 | : | 1 | = | 7 | remainder ( 0 ) | ||||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.