Find Greatest Common Divisor of 44 and 36, using Euclidean algorithm.
Answer
The GCD of given numbers is 4.
Explanation
Step 1 :
Divide $ 44 $ by $ 36 $ and get the remainder
The remainder is positive ($ 8 > 0 $), so we will continue with division.
Step 2 :
Divide $ 36 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 3 :
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.
| 44 | : | 36 | = | 1 | remainder ( 8 ) | ||||
| 36 | : | 8 | = | 4 | 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.
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