Find Greatest Common Divisor of 1299 and 1599, using Euclidean algorithm.
Answer
The GCD of given numbers is 3.
Explanation
Step 1 :
Divide $ 1599 $ by $ 1299 $ and get the remainder
The remainder is positive ($ 300 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1299 $ by $ \color{blue}{ 300 } $ and get the remainder
The remainder is still positive ($ 99 > 0 $), so we will continue with division.
Step 3 :
Divide $ 300 $ by $ \color{blue}{ 99 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 4 :
Divide $ 99 $ 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.
| 1599 | : | 1299 | = | 1 | remainder ( 300 ) | ||||||
| 1299 | : | 300 | = | 4 | remainder ( 99 ) | ||||||
| 300 | : | 99 | = | 3 | remainder ( 3 ) | ||||||
| 99 | : | 3 | = | 33 | remainder ( 0 ) | ||||||
| GCD = 3 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.