The GCD of given numbers is 3.
Step 1 :
Divide $ 222 $ by $ 159 $ and get the remainder
The remainder is positive ($ 63 > 0 $), so we will continue with division.
Step 2 :
Divide $ 159 $ by $ \color{blue}{ 63 } $ and get the remainder
The remainder is still positive ($ 33 > 0 $), so we will continue with division.
Step 3 :
Divide $ 63 $ by $ \color{blue}{ 33 } $ and get the remainder
The remainder is still positive ($ 30 > 0 $), so we will continue with division.
Step 4 :
Divide $ 33 $ by $ \color{blue}{ 30 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 5 :
Divide $ 30 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 3 }} $.
We can summarize an algorithm into a following table.
222 | : | 159 | = | 1 | remainder ( 63 ) | ||||||||
159 | : | 63 | = | 2 | remainder ( 33 ) | ||||||||
63 | : | 33 | = | 1 | remainder ( 30 ) | ||||||||
33 | : | 30 | = | 1 | remainder ( 3 ) | ||||||||
30 | : | 3 | = | 10 | remainder ( 0 ) | ||||||||
GCD = 3 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.