Find Greatest Common Divisor of 96 and 62, using Euclidean algorithm.
Answer
The GCD of given numbers is 2.
Explanation
Step 1 :
Divide $ 96 $ by $ 62 $ and get the remainder
The remainder is positive ($ 34 > 0 $), so we will continue with division.
Step 2 :
Divide $ 62 $ by $ \color{blue}{ 34 } $ and get the remainder
The remainder is still positive ($ 28 > 0 $), so we will continue with division.
Step 3 :
Divide $ 34 $ by $ \color{blue}{ 28 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 4 :
Divide $ 28 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 5 :
Divide $ 6 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 6 :
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.
| 96 | : | 62 | = | 1 | remainder ( 34 ) | ||||||||||
| 62 | : | 34 | = | 1 | remainder ( 28 ) | ||||||||||
| 34 | : | 28 | = | 1 | remainder ( 6 ) | ||||||||||
| 28 | : | 6 | = | 4 | 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.