Find Greatest Common Divisor of 34709 and 100313, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 100313 $ by $ 34709 $ and get the remainder
The remainder is positive ($ 30895 > 0 $), so we will continue with division.
Step 2 :
Divide $ 34709 $ by $ \color{blue}{ 30895 } $ and get the remainder
The remainder is still positive ($ 3814 > 0 $), so we will continue with division.
Step 3 :
Divide $ 30895 $ by $ \color{blue}{ 3814 } $ and get the remainder
The remainder is still positive ($ 383 > 0 $), so we will continue with division.
Step 4 :
Divide $ 3814 $ by $ \color{blue}{ 383 } $ and get the remainder
The remainder is still positive ($ 367 > 0 $), so we will continue with division.
Step 5 :
Divide $ 383 $ by $ \color{blue}{ 367 } $ and get the remainder
The remainder is still positive ($ 16 > 0 $), so we will continue with division.
Step 6 :
Divide $ 367 $ by $ \color{blue}{ 16 } $ and get the remainder
The remainder is still positive ($ 15 > 0 $), so we will continue with division.
Step 7 :
Divide $ 16 $ by $ \color{blue}{ 15 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 8 :
Divide $ 15 $ 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.
| 100313 | : | 34709 | = | 2 | remainder ( 30895 ) | ||||||||||||||
| 34709 | : | 30895 | = | 1 | remainder ( 3814 ) | ||||||||||||||
| 30895 | : | 3814 | = | 8 | remainder ( 383 ) | ||||||||||||||
| 3814 | : | 383 | = | 9 | remainder ( 367 ) | ||||||||||||||
| 383 | : | 367 | = | 1 | remainder ( 16 ) | ||||||||||||||
| 367 | : | 16 | = | 22 | remainder ( 15 ) | ||||||||||||||
| 16 | : | 15 | = | 1 | remainder ( 1 ) | ||||||||||||||
| 15 | : | 1 | = | 15 | remainder ( 0 ) | ||||||||||||||
| GCD = 1 | |||||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.