Find Greatest Common Divisor of 3532 and 3288, using Euclidean algorithm.
Answer
The GCD of given numbers is 4.
Explanation
Step 1 :
Divide $ 3532 $ by $ 3288 $ and get the remainder
The remainder is positive ($ 244 > 0 $), so we will continue with division.
Step 2 :
Divide $ 3288 $ by $ \color{blue}{ 244 } $ and get the remainder
The remainder is still positive ($ 116 > 0 $), so we will continue with division.
Step 3 :
Divide $ 244 $ by $ \color{blue}{ 116 } $ and get the remainder
The remainder is still positive ($ 12 > 0 $), so we will continue with division.
Step 4 :
Divide $ 116 $ by $ \color{blue}{ 12 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 5 :
Divide $ 12 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 6 :
Divide $ 8 $ 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.
| 3532 | : | 3288 | = | 1 | remainder ( 244 ) | ||||||||||
| 3288 | : | 244 | = | 13 | remainder ( 116 ) | ||||||||||
| 244 | : | 116 | = | 2 | remainder ( 12 ) | ||||||||||
| 116 | : | 12 | = | 9 | remainder ( 8 ) | ||||||||||
| 12 | : | 8 | = | 1 | remainder ( 4 ) | ||||||||||
| 8 | : | 4 | = | 2 | remainder ( 0 ) | ||||||||||
| GCD = 4 | |||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.