Find Greatest Common Divisor of 324 and 68, using Euclidean algorithm.
Answer
The GCD of given numbers is 4.
Explanation
Step 1 :
Divide $ 324 $ by $ 68 $ and get the remainder
The remainder is positive ($ 52 > 0 $), so we will continue with division.
Step 2 :
Divide $ 68 $ by $ \color{blue}{ 52 } $ and get the remainder
The remainder is still positive ($ 16 > 0 $), so we will continue with division.
Step 3 :
Divide $ 52 $ by $ \color{blue}{ 16 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 4 :
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.
| 324 | : | 68 | = | 4 | remainder ( 52 ) | ||||||
| 68 | : | 52 | = | 1 | remainder ( 16 ) | ||||||
| 52 | : | 16 | = | 3 | 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.