The GCD of given numbers is 44.
Step 1 :
Divide $ 2024 $ by $ 572 $ and get the remainder
The remainder is positive ($ 308 > 0 $), so we will continue with division.
Step 2 :
Divide $ 572 $ by $ \color{blue}{ 308 } $ and get the remainder
The remainder is still positive ($ 264 > 0 $), so we will continue with division.
Step 3 :
Divide $ 308 $ by $ \color{blue}{ 264 } $ and get the remainder
The remainder is still positive ($ 44 > 0 $), so we will continue with division.
Step 4 :
Divide $ 264 $ by $ \color{blue}{ 44 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 44 }} $.
We can summarize an algorithm into a following table.
2024 | : | 572 | = | 3 | remainder ( 308 ) | ||||||
572 | : | 308 | = | 1 | remainder ( 264 ) | ||||||
308 | : | 264 | = | 1 | remainder ( 44 ) | ||||||
264 | : | 44 | = | 6 | remainder ( 0 ) | ||||||
GCD = 44 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.