Find Greatest Common Divisor of 3219 and 74, using Euclidean algorithm.
Answer
The GCD of given numbers is 37.
Explanation
Step 1 :
Divide $ 3219 $ by $ 74 $ and get the remainder
The remainder is positive ($ 37 > 0 $), so we will continue with division.
Step 2 :
Divide $ 74 $ by $ \color{blue}{ 37 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 37 }} $.
We can summarize an algorithm into a following table.
| 3219 | : | 74 | = | 43 | remainder ( 37 ) | ||
| 74 | : | 37 | = | 2 | remainder ( 0 ) | ||
| GCD = 37 | |||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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