Find Greatest Common Divisor of 332 and 128, using Euclidean algorithm.
Answer
The GCD of given numbers is 4.
Explanation
Step 1 :
Divide $ 332 $ by $ 128 $ and get the remainder
The remainder is positive ($ 76 > 0 $), so we will continue with division.
Step 2 :
Divide $ 128 $ by $ \color{blue}{ 76 } $ and get the remainder
The remainder is still positive ($ 52 > 0 $), so we will continue with division.
Step 3 :
Divide $ 76 $ by $ \color{blue}{ 52 } $ and get the remainder
The remainder is still positive ($ 24 > 0 $), so we will continue with division.
Step 4 :
Divide $ 52 $ by $ \color{blue}{ 24 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 5 :
Divide $ 24 $ 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.
| 332 | : | 128 | = | 2 | remainder ( 76 ) | ||||||||
| 128 | : | 76 | = | 1 | remainder ( 52 ) | ||||||||
| 76 | : | 52 | = | 1 | remainder ( 24 ) | ||||||||
| 52 | : | 24 | = | 2 | remainder ( 4 ) | ||||||||
| 24 | : | 4 | = | 6 | remainder ( 0 ) | ||||||||
| GCD = 4 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.