The GCD of given numbers is 13.
Step 1 :
Divide $ 221 $ by $ 143 $ and get the remainder
The remainder is positive ($ 78 > 0 $), so we will continue with division.
Step 2 :
Divide $ 143 $ by $ \color{blue}{ 78 } $ and get the remainder
The remainder is still positive ($ 65 > 0 $), so we will continue with division.
Step 3 :
Divide $ 78 $ by $ \color{blue}{ 65 } $ and get the remainder
The remainder is still positive ($ 13 > 0 $), so we will continue with division.
Step 4 :
Divide $ 65 $ by $ \color{blue}{ 13 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 13 }} $.
We can summarize an algorithm into a following table.
221 | : | 143 | = | 1 | remainder ( 78 ) | ||||||
143 | : | 78 | = | 1 | remainder ( 65 ) | ||||||
78 | : | 65 | = | 1 | remainder ( 13 ) | ||||||
65 | : | 13 | = | 5 | remainder ( 0 ) | ||||||
GCD = 13 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.