The GCD of given numbers is 1.
Step 1 :
Divide $ 72345 $ by $ 4321 $ and get the remainder
The remainder is positive ($ 3209 > 0 $), so we will continue with division.
Step 2 :
Divide $ 4321 $ by $ \color{blue}{ 3209 } $ and get the remainder
The remainder is still positive ($ 1112 > 0 $), so we will continue with division.
Step 3 :
Divide $ 3209 $ by $ \color{blue}{ 1112 } $ and get the remainder
The remainder is still positive ($ 985 > 0 $), so we will continue with division.
Step 4 :
Divide $ 1112 $ by $ \color{blue}{ 985 } $ and get the remainder
The remainder is still positive ($ 127 > 0 $), so we will continue with division.
Step 5 :
Divide $ 985 $ by $ \color{blue}{ 127 } $ and get the remainder
The remainder is still positive ($ 96 > 0 $), so we will continue with division.
Step 6 :
Divide $ 127 $ by $ \color{blue}{ 96 } $ and get the remainder
The remainder is still positive ($ 31 > 0 $), so we will continue with division.
Step 7 :
Divide $ 96 $ by $ \color{blue}{ 31 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 8 :
Divide $ 31 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 9 :
Divide $ 3 $ 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.
72345 | : | 4321 | = | 16 | remainder ( 3209 ) | ||||||||||||||||
4321 | : | 3209 | = | 1 | remainder ( 1112 ) | ||||||||||||||||
3209 | : | 1112 | = | 2 | remainder ( 985 ) | ||||||||||||||||
1112 | : | 985 | = | 1 | remainder ( 127 ) | ||||||||||||||||
985 | : | 127 | = | 7 | remainder ( 96 ) | ||||||||||||||||
127 | : | 96 | = | 1 | remainder ( 31 ) | ||||||||||||||||
96 | : | 31 | = | 3 | remainder ( 3 ) | ||||||||||||||||
31 | : | 3 | = | 10 | remainder ( 1 ) | ||||||||||||||||
3 | : | 1 | = | 3 | remainder ( 0 ) | ||||||||||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.