The GCD of given numbers is 1.
Step 1 :
Divide $ 23883 $ by $ 12409 $ and get the remainder
The remainder is positive ($ 11474 > 0 $), so we will continue with division.
Step 2 :
Divide $ 12409 $ by $ \color{blue}{ 11474 } $ and get the remainder
The remainder is still positive ($ 935 > 0 $), so we will continue with division.
Step 3 :
Divide $ 11474 $ by $ \color{blue}{ 935 } $ and get the remainder
The remainder is still positive ($ 254 > 0 $), so we will continue with division.
Step 4 :
Divide $ 935 $ by $ \color{blue}{ 254 } $ and get the remainder
The remainder is still positive ($ 173 > 0 $), so we will continue with division.
Step 5 :
Divide $ 254 $ by $ \color{blue}{ 173 } $ and get the remainder
The remainder is still positive ($ 81 > 0 $), so we will continue with division.
Step 6 :
Divide $ 173 $ by $ \color{blue}{ 81 } $ and get the remainder
The remainder is still positive ($ 11 > 0 $), so we will continue with division.
Step 7 :
Divide $ 81 $ by $ \color{blue}{ 11 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 8 :
Divide $ 11 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 9 :
Divide $ 4 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 10 :
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.
23883 | : | 12409 | = | 1 | remainder ( 11474 ) | ||||||||||||||||||
12409 | : | 11474 | = | 1 | remainder ( 935 ) | ||||||||||||||||||
11474 | : | 935 | = | 12 | remainder ( 254 ) | ||||||||||||||||||
935 | : | 254 | = | 3 | remainder ( 173 ) | ||||||||||||||||||
254 | : | 173 | = | 1 | remainder ( 81 ) | ||||||||||||||||||
173 | : | 81 | = | 2 | remainder ( 11 ) | ||||||||||||||||||
81 | : | 11 | = | 7 | remainder ( 4 ) | ||||||||||||||||||
11 | : | 4 | = | 2 | remainder ( 3 ) | ||||||||||||||||||
4 | : | 3 | = | 1 | 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.