Find Greatest Common Divisor of 76584 and 836, using Euclidean algorithm.
Answer
The GCD of given numbers is 4.
Explanation
Step 1 :
Divide $ 76584 $ by $ 836 $ and get the remainder
The remainder is positive ($ 508 > 0 $), so we will continue with division.
Step 2 :
Divide $ 836 $ by $ \color{blue}{ 508 } $ and get the remainder
The remainder is still positive ($ 328 > 0 $), so we will continue with division.
Step 3 :
Divide $ 508 $ by $ \color{blue}{ 328 } $ and get the remainder
The remainder is still positive ($ 180 > 0 $), so we will continue with division.
Step 4 :
Divide $ 328 $ by $ \color{blue}{ 180 } $ and get the remainder
The remainder is still positive ($ 148 > 0 $), so we will continue with division.
Step 5 :
Divide $ 180 $ by $ \color{blue}{ 148 } $ and get the remainder
The remainder is still positive ($ 32 > 0 $), so we will continue with division.
Step 6 :
Divide $ 148 $ by $ \color{blue}{ 32 } $ and get the remainder
The remainder is still positive ($ 20 > 0 $), so we will continue with division.
Step 7 :
Divide $ 32 $ by $ \color{blue}{ 20 } $ and get the remainder
The remainder is still positive ($ 12 > 0 $), so we will continue with division.
Step 8 :
Divide $ 20 $ by $ \color{blue}{ 12 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 9 :
Divide $ 12 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 10 :
Divide $ 8 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 4 }} $.
We can summarize an algorithm into a following table.
| 76584 | : | 836 | = | 91 | remainder ( 508 ) | ||||||||||||||||||
| 836 | : | 508 | = | 1 | remainder ( 328 ) | ||||||||||||||||||
| 508 | : | 328 | = | 1 | remainder ( 180 ) | ||||||||||||||||||
| 328 | : | 180 | = | 1 | remainder ( 148 ) | ||||||||||||||||||
| 180 | : | 148 | = | 1 | remainder ( 32 ) | ||||||||||||||||||
| 148 | : | 32 | = | 4 | remainder ( 20 ) | ||||||||||||||||||
| 32 | : | 20 | = | 1 | remainder ( 12 ) | ||||||||||||||||||
| 20 | : | 12 | = | 1 | remainder ( 8 ) | ||||||||||||||||||
| 12 | : | 8 | = | 1 | remainder ( 4 ) | ||||||||||||||||||
| 8 | : | 4 | = | 2 | remainder ( 0 ) | ||||||||||||||||||
| GCD = 4 | |||||||||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.