Find Greatest Common Divisor of 291 and 252, using Euclidean algorithm.
Answer
The GCD of given numbers is 3.
Explanation
Step 1 :
Divide $ 291 $ by $ 252 $ and get the remainder
The remainder is positive ($ 39 > 0 $), so we will continue with division.
Step 2 :
Divide $ 252 $ by $ \color{blue}{ 39 } $ and get the remainder
The remainder is still positive ($ 18 > 0 $), so we will continue with division.
Step 3 :
Divide $ 39 $ by $ \color{blue}{ 18 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 4 :
Divide $ 18 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 3 }} $.
We can summarize an algorithm into a following table.
| 291 | : | 252 | = | 1 | remainder ( 39 ) | ||||||
| 252 | : | 39 | = | 6 | remainder ( 18 ) | ||||||
| 39 | : | 18 | = | 2 | remainder ( 3 ) | ||||||
| 18 | : | 3 | = | 6 | remainder ( 0 ) | ||||||
| GCD = 3 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.