Find Greatest Common Divisor of 72 and 52, using Euclidean algorithm.
Answer
The GCD of given numbers is 4.
Explanation
Step 1 :
Divide $ 72 $ by $ 52 $ and get the remainder
The remainder is positive ($ 20 > 0 $), so we will continue with division.
Step 2 :
Divide $ 52 $ by $ \color{blue}{ 20 } $ and get the remainder
The remainder is still positive ($ 12 > 0 $), so we will continue with division.
Step 3 :
Divide $ 20 $ by $ \color{blue}{ 12 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 4 :
Divide $ 12 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 5 :
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.
| 72 | : | 52 | = | 1 | remainder ( 20 ) | ||||||||
| 52 | : | 20 | = | 2 | remainder ( 12 ) | ||||||||
| 20 | : | 12 | = | 1 | 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.