Find Greatest Common Divisor of 7429 and 33649, using Euclidean algorithm.
Answer
The GCD of given numbers is 437.
Explanation
Step 1 :
Divide $ 33649 $ by $ 7429 $ and get the remainder
The remainder is positive ($ 3933 > 0 $), so we will continue with division.
Step 2 :
Divide $ 7429 $ by $ \color{blue}{ 3933 } $ and get the remainder
The remainder is still positive ($ 3496 > 0 $), so we will continue with division.
Step 3 :
Divide $ 3933 $ by $ \color{blue}{ 3496 } $ and get the remainder
The remainder is still positive ($ 437 > 0 $), so we will continue with division.
Step 4 :
Divide $ 3496 $ by $ \color{blue}{ 437 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 437 }} $.
We can summarize an algorithm into a following table.
| 33649 | : | 7429 | = | 4 | remainder ( 3933 ) | ||||||
| 7429 | : | 3933 | = | 1 | remainder ( 3496 ) | ||||||
| 3933 | : | 3496 | = | 1 | remainder ( 437 ) | ||||||
| 3496 | : | 437 | = | 8 | remainder ( 0 ) | ||||||
| GCD = 437 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.