Find Greatest Common Divisor of 4076 and 1024, using Euclidean algorithm.
Answer
The GCD of given numbers is 4.
Explanation
Step 1 :
Divide $ 4076 $ by $ 1024 $ and get the remainder
The remainder is positive ($ 1004 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1024 $ by $ \color{blue}{ 1004 } $ and get the remainder
The remainder is still positive ($ 20 > 0 $), so we will continue with division.
Step 3 :
Divide $ 1004 $ by $ \color{blue}{ 20 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 4 :
Divide $ 20 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 4 }} $.
We can summarize an algorithm into a following table.
| 4076 | : | 1024 | = | 3 | remainder ( 1004 ) | ||||||
| 1024 | : | 1004 | = | 1 | remainder ( 20 ) | ||||||
| 1004 | : | 20 | = | 50 | remainder ( 4 ) | ||||||
| 20 | : | 4 | = | 5 | remainder ( 0 ) | ||||||
| GCD = 4 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.