Find Greatest Common Divisor of 56 and 72, using Euclidean algorithm.
Answer
The GCD of given numbers is 8.
Explanation
Step 1 :
Divide $ 72 $ by $ 56 $ and get the remainder
The remainder is positive ($ 16 > 0 $), so we will continue with division.
Step 2 :
Divide $ 56 $ by $ \color{blue}{ 16 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 3 :
Divide $ 16 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 8 }} $.
We can summarize an algorithm into a following table.
| 72 | : | 56 | = | 1 | remainder ( 16 ) | ||||
| 56 | : | 16 | = | 3 | remainder ( 8 ) | ||||
| 16 | : | 8 | = | 2 | remainder ( 0 ) | ||||
| GCD = 8 | |||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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