The GCD of given numbers is 29.
Step 1 :
Divide $ 2349 $ by $ 1537 $ and get the remainder
The remainder is positive ($ 812 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1537 $ by $ \color{blue}{ 812 } $ and get the remainder
The remainder is still positive ($ 725 > 0 $), so we will continue with division.
Step 3 :
Divide $ 812 $ by $ \color{blue}{ 725 } $ and get the remainder
The remainder is still positive ($ 87 > 0 $), so we will continue with division.
Step 4 :
Divide $ 725 $ by $ \color{blue}{ 87 } $ and get the remainder
The remainder is still positive ($ 29 > 0 $), so we will continue with division.
Step 5 :
Divide $ 87 $ 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.
2349 | : | 1537 | = | 1 | remainder ( 812 ) | ||||||||
1537 | : | 812 | = | 1 | remainder ( 725 ) | ||||||||
812 | : | 725 | = | 1 | remainder ( 87 ) | ||||||||
725 | : | 87 | = | 8 | remainder ( 29 ) | ||||||||
87 | : | 29 | = | 3 | remainder ( 0 ) | ||||||||
GCD = 29 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.