Find Greatest Common Divisor of 1404 and 455, using Euclidean algorithm.
Answer
The GCD of given numbers is 13.
Explanation
Step 1 :
Divide $ 1404 $ by $ 455 $ and get the remainder
The remainder is positive ($ 39 > 0 $), so we will continue with division.
Step 2 :
Divide $ 455 $ by $ \color{blue}{ 39 } $ and get the remainder
The remainder is still positive ($ 26 > 0 $), so we will continue with division.
Step 3 :
Divide $ 39 $ by $ \color{blue}{ 26 } $ and get the remainder
The remainder is still positive ($ 13 > 0 $), so we will continue with division.
Step 4 :
Divide $ 26 $ by $ \color{blue}{ 13 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 13 }} $.
We can summarize an algorithm into a following table.
| 1404 | : | 455 | = | 3 | remainder ( 39 ) | ||||||
| 455 | : | 39 | = | 11 | remainder ( 26 ) | ||||||
| 39 | : | 26 | = | 1 | remainder ( 13 ) | ||||||
| 26 | : | 13 | = | 2 | remainder ( 0 ) | ||||||
| GCD = 13 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.