Find Greatest Common Divisor of 72 and 47, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 72 $ by $ 47 $ and get the remainder
The remainder is positive ($ 25 > 0 $), so we will continue with division.
Step 2 :
Divide $ 47 $ by $ \color{blue}{ 25 } $ and get the remainder
The remainder is still positive ($ 22 > 0 $), so we will continue with division.
Step 3 :
Divide $ 25 $ by $ \color{blue}{ 22 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 4 :
Divide $ 22 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 5 :
Divide $ 3 $ by $ \color{blue}{ 1 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.
We can summarize an algorithm into a following table.
| 72 | : | 47 | = | 1 | remainder ( 25 ) | ||||||||
| 47 | : | 25 | = | 1 | remainder ( 22 ) | ||||||||
| 25 | : | 22 | = | 1 | remainder ( 3 ) | ||||||||
| 22 | : | 3 | = | 7 | remainder ( 1 ) | ||||||||
| 3 | : | 1 | = | 3 | remainder ( 0 ) | ||||||||
| GCD = 1 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.