Find Greatest Common Divisor of 332 and 192, using Euclidean algorithm.
Answer
The GCD of given numbers is 4.
Explanation
Step 1 :
Divide $ 332 $ by $ 192 $ and get the remainder
The remainder is positive ($ 140 > 0 $), so we will continue with division.
Step 2 :
Divide $ 192 $ by $ \color{blue}{ 140 } $ and get the remainder
The remainder is still positive ($ 52 > 0 $), so we will continue with division.
Step 3 :
Divide $ 140 $ by $ \color{blue}{ 52 } $ and get the remainder
The remainder is still positive ($ 36 > 0 $), so we will continue with division.
Step 4 :
Divide $ 52 $ by $ \color{blue}{ 36 } $ and get the remainder
The remainder is still positive ($ 16 > 0 $), so we will continue with division.
Step 5 :
Divide $ 36 $ by $ \color{blue}{ 16 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 6 :
Divide $ 16 $ 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 | : | 192 | = | 1 | remainder ( 140 ) | ||||||||||
| 192 | : | 140 | = | 1 | remainder ( 52 ) | ||||||||||
| 140 | : | 52 | = | 2 | remainder ( 36 ) | ||||||||||
| 52 | : | 36 | = | 1 | remainder ( 16 ) | ||||||||||
| 36 | : | 16 | = | 2 | remainder ( 4 ) | ||||||||||
| 16 | : | 4 | = | 4 | remainder ( 0 ) | ||||||||||
| GCD = 4 | |||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.