Find Greatest Common Divisor of 16 and 31, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 31 $ by $ 16 $ and get the remainder
The remainder is positive ($ 15 > 0 $), so we will continue with division.
Step 2 :
Divide $ 16 $ by $ \color{blue}{ 15 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 3 :
Divide $ 15 $ by $ \color{blue}{ 1 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.
We can summarize an algorithm into a following table.
| 31 | : | 16 | = | 1 | remainder ( 15 ) | ||||
| 16 | : | 15 | = | 1 | remainder ( 1 ) | ||||
| 15 | : | 1 | = | 15 | remainder ( 0 ) | ||||
| GCD = 1 | |||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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