Find Greatest Common Divisor of 32 and 74, using Euclidean algorithm.
Answer
The GCD of given numbers is 2.
Explanation
Step 1 :
Divide $ 74 $ by $ 32 $ and get the remainder
The remainder is positive ($ 10 > 0 $), so we will continue with division.
Step 2 :
Divide $ 32 $ by $ \color{blue}{ 10 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 3 :
Divide $ 10 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 2 }} $.
We can summarize an algorithm into a following table.
| 74 | : | 32 | = | 2 | remainder ( 10 ) | ||||
| 32 | : | 10 | = | 3 | remainder ( 2 ) | ||||
| 10 | : | 2 | = | 5 | remainder ( 0 ) | ||||
| GCD = 2 | |||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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