The GCD of given numbers is 29.
Step 1 :
Divide $ 232 $ by $ 145 $ and get the remainder
The remainder is positive ($ 87 > 0 $), so we will continue with division.
Step 2 :
Divide $ 145 $ by $ \color{blue}{ 87 } $ and get the remainder
The remainder is still positive ($ 58 > 0 $), so we will continue with division.
Step 3 :
Divide $ 87 $ by $ \color{blue}{ 58 } $ and get the remainder
The remainder is still positive ($ 29 > 0 $), so we will continue with division.
Step 4 :
Divide $ 58 $ by $ \color{blue}{ 29 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 29 }} $.
We can summarize an algorithm into a following table.
232 | : | 145 | = | 1 | remainder ( 87 ) | ||||||
145 | : | 87 | = | 1 | remainder ( 58 ) | ||||||
87 | : | 58 | = | 1 | remainder ( 29 ) | ||||||
58 | : | 29 | = | 2 | remainder ( 0 ) | ||||||
GCD = 29 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.