Find Greatest Common Divisor of 52 and 98, using Euclidean algorithm.
Answer
The GCD of given numbers is 2.
Explanation
Step 1 :
Divide $ 98 $ by $ 52 $ and get the remainder
The remainder is positive ($ 46 > 0 $), so we will continue with division.
Step 2 :
Divide $ 52 $ by $ \color{blue}{ 46 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 3 :
Divide $ 46 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 4 :
Divide $ 6 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 5 :
Divide $ 4 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 2 }} $.
We can summarize an algorithm into a following table.
| 98 | : | 52 | = | 1 | remainder ( 46 ) | ||||||||
| 52 | : | 46 | = | 1 | remainder ( 6 ) | ||||||||
| 46 | : | 6 | = | 7 | remainder ( 4 ) | ||||||||
| 6 | : | 4 | = | 1 | remainder ( 2 ) | ||||||||
| 4 | : | 2 | = | 2 | remainder ( 0 ) | ||||||||
| GCD = 2 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.