Find Greatest Common Divisor of 53 and 28, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 53 $ by $ 28 $ and get the remainder
The remainder is positive ($ 25 > 0 $), so we will continue with division.
Step 2 :
Divide $ 28 $ by $ \color{blue}{ 25 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 3 :
Divide $ 25 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 4 :
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.
| 53 | : | 28 | = | 1 | remainder ( 25 ) | ||||||
| 28 | : | 25 | = | 1 | remainder ( 3 ) | ||||||
| 25 | : | 3 | = | 8 | 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.