The GCD of given numbers is 1.
Step 1 :
Divide $ 728 $ by $ 125 $ and get the remainder
The remainder is positive ($ 103 > 0 $), so we will continue with division.
Step 2 :
Divide $ 125 $ by $ \color{blue}{ 103 } $ and get the remainder
The remainder is still positive ($ 22 > 0 $), so we will continue with division.
Step 3 :
Divide $ 103 $ by $ \color{blue}{ 22 } $ and get the remainder
The remainder is still positive ($ 15 > 0 $), so we will continue with division.
Step 4 :
Divide $ 22 $ by $ \color{blue}{ 15 } $ and get the remainder
The remainder is still positive ($ 7 > 0 $), so we will continue with division.
Step 5 :
Divide $ 15 $ by $ \color{blue}{ 7 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 6 :
Divide $ 7 $ by $ \color{blue}{ 1 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.
We can summarize an algorithm into a following table.
728 | : | 125 | = | 5 | remainder ( 103 ) | ||||||||||
125 | : | 103 | = | 1 | remainder ( 22 ) | ||||||||||
103 | : | 22 | = | 4 | remainder ( 15 ) | ||||||||||
22 | : | 15 | = | 1 | remainder ( 7 ) | ||||||||||
15 | : | 7 | = | 2 | remainder ( 1 ) | ||||||||||
7 | : | 1 | = | 7 | remainder ( 0 ) | ||||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.