The GCD of given numbers is 1.
Step 1 :
Divide $ 7469 $ by $ 4369 $ and get the remainder
The remainder is positive ($ 3100 > 0 $), so we will continue with division.
Step 2 :
Divide $ 4369 $ by $ \color{blue}{ 3100 } $ and get the remainder
The remainder is still positive ($ 1269 > 0 $), so we will continue with division.
Step 3 :
Divide $ 3100 $ by $ \color{blue}{ 1269 } $ and get the remainder
The remainder is still positive ($ 562 > 0 $), so we will continue with division.
Step 4 :
Divide $ 1269 $ by $ \color{blue}{ 562 } $ and get the remainder
The remainder is still positive ($ 145 > 0 $), so we will continue with division.
Step 5 :
Divide $ 562 $ by $ \color{blue}{ 145 } $ and get the remainder
The remainder is still positive ($ 127 > 0 $), so we will continue with division.
Step 6 :
Divide $ 145 $ by $ \color{blue}{ 127 } $ and get the remainder
The remainder is still positive ($ 18 > 0 $), so we will continue with division.
Step 7 :
Divide $ 127 $ by $ \color{blue}{ 18 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 8 :
Divide $ 18 $ 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.
7469 | : | 4369 | = | 1 | remainder ( 3100 ) | ||||||||||||||
4369 | : | 3100 | = | 1 | remainder ( 1269 ) | ||||||||||||||
3100 | : | 1269 | = | 2 | remainder ( 562 ) | ||||||||||||||
1269 | : | 562 | = | 2 | remainder ( 145 ) | ||||||||||||||
562 | : | 145 | = | 3 | remainder ( 127 ) | ||||||||||||||
145 | : | 127 | = | 1 | remainder ( 18 ) | ||||||||||||||
127 | : | 18 | = | 7 | remainder ( 1 ) | ||||||||||||||
18 | : | 1 | = | 18 | remainder ( 0 ) | ||||||||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.