Find Greatest Common Divisor of 2024 and 748, using Euclidean algorithm.
Answer
The GCD of given numbers is 44.
Explanation
Step 1 :
Divide $ 2024 $ by $ 748 $ and get the remainder
The remainder is positive ($ 528 > 0 $), so we will continue with division.
Step 2 :
Divide $ 748 $ by $ \color{blue}{ 528 } $ and get the remainder
The remainder is still positive ($ 220 > 0 $), so we will continue with division.
Step 3 :
Divide $ 528 $ by $ \color{blue}{ 220 } $ and get the remainder
The remainder is still positive ($ 88 > 0 $), so we will continue with division.
Step 4 :
Divide $ 220 $ by $ \color{blue}{ 88 } $ and get the remainder
The remainder is still positive ($ 44 > 0 $), so we will continue with division.
Step 5 :
Divide $ 88 $ 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 | : | 748 | = | 2 | remainder ( 528 ) | ||||||||
| 748 | : | 528 | = | 1 | remainder ( 220 ) | ||||||||
| 528 | : | 220 | = | 2 | remainder ( 88 ) | ||||||||
| 220 | : | 88 | = | 2 | remainder ( 44 ) | ||||||||
| 88 | : | 44 | = | 2 | remainder ( 0 ) | ||||||||
| GCD = 44 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.