The GCD of given numbers is 1.
Step 1 :
Divide $ 2024 $ by $ 1061 $ and get the remainder
The remainder is positive ($ 963 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1061 $ by $ \color{blue}{ 963 } $ and get the remainder
The remainder is still positive ($ 98 > 0 $), so we will continue with division.
Step 3 :
Divide $ 963 $ by $ \color{blue}{ 98 } $ and get the remainder
The remainder is still positive ($ 81 > 0 $), so we will continue with division.
Step 4 :
Divide $ 98 $ by $ \color{blue}{ 81 } $ and get the remainder
The remainder is still positive ($ 17 > 0 $), so we will continue with division.
Step 5 :
Divide $ 81 $ by $ \color{blue}{ 17 } $ and get the remainder
The remainder is still positive ($ 13 > 0 $), so we will continue with division.
Step 6 :
Divide $ 17 $ by $ \color{blue}{ 13 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 7 :
Divide $ 13 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 8 :
Divide $ 4 $ 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.
2024 | : | 1061 | = | 1 | remainder ( 963 ) | ||||||||||||||
1061 | : | 963 | = | 1 | remainder ( 98 ) | ||||||||||||||
963 | : | 98 | = | 9 | remainder ( 81 ) | ||||||||||||||
98 | : | 81 | = | 1 | remainder ( 17 ) | ||||||||||||||
81 | : | 17 | = | 4 | remainder ( 13 ) | ||||||||||||||
17 | : | 13 | = | 1 | remainder ( 4 ) | ||||||||||||||
13 | : | 4 | = | 3 | remainder ( 1 ) | ||||||||||||||
4 | : | 1 | = | 4 | remainder ( 0 ) | ||||||||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.