The GCD of given numbers is 23.
Step 1 :
Divide $ 644 $ by $ 115 $ and get the remainder
The remainder is positive ($ 69 > 0 $), so we will continue with division.
Step 2 :
Divide $ 115 $ by $ \color{blue}{ 69 } $ and get the remainder
The remainder is still positive ($ 46 > 0 $), so we will continue with division.
Step 3 :
Divide $ 69 $ by $ \color{blue}{ 46 } $ and get the remainder
The remainder is still positive ($ 23 > 0 $), so we will continue with division.
Step 4 :
Divide $ 46 $ by $ \color{blue}{ 23 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 23 }} $.
We can summarize an algorithm into a following table.
644 | : | 115 | = | 5 | remainder ( 69 ) | ||||||
115 | : | 69 | = | 1 | remainder ( 46 ) | ||||||
69 | : | 46 | = | 1 | remainder ( 23 ) | ||||||
46 | : | 23 | = | 2 | remainder ( 0 ) | ||||||
GCD = 23 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.