The GCD of given numbers is 7.
Step 1 :
Divide $ 52598 $ by $ 2541 $ and get the remainder
The remainder is positive ($ 1778 > 0 $), so we will continue with division.
Step 2 :
Divide $ 2541 $ by $ \color{blue}{ 1778 } $ and get the remainder
The remainder is still positive ($ 763 > 0 $), so we will continue with division.
Step 3 :
Divide $ 1778 $ by $ \color{blue}{ 763 } $ and get the remainder
The remainder is still positive ($ 252 > 0 $), so we will continue with division.
Step 4 :
Divide $ 763 $ by $ \color{blue}{ 252 } $ and get the remainder
The remainder is still positive ($ 7 > 0 $), so we will continue with division.
Step 5 :
Divide $ 252 $ by $ \color{blue}{ 7 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 7 }} $.
We can summarize an algorithm into a following table.
52598 | : | 2541 | = | 20 | remainder ( 1778 ) | ||||||||
2541 | : | 1778 | = | 1 | remainder ( 763 ) | ||||||||
1778 | : | 763 | = | 2 | remainder ( 252 ) | ||||||||
763 | : | 252 | = | 3 | remainder ( 7 ) | ||||||||
252 | : | 7 | = | 36 | remainder ( 0 ) | ||||||||
GCD = 7 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.