Find Greatest Common Divisor of 120 and 84, using Euclidean algorithm.
Answer
The GCD of given numbers is 12.
Explanation
Step 1 :
Divide $ 120 $ by $ 84 $ and get the remainder
The remainder is positive ($ 36 > 0 $), so we will continue with division.
Step 2 :
Divide $ 84 $ by $ \color{blue}{ 36 } $ and get the remainder
The remainder is still positive ($ 12 > 0 $), so we will continue with division.
Step 3 :
Divide $ 36 $ by $ \color{blue}{ 12 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 12 }} $.
We can summarize an algorithm into a following table.
| 120 | : | 84 | = | 1 | remainder ( 36 ) | ||||
| 84 | : | 36 | = | 2 | remainder ( 12 ) | ||||
| 36 | : | 12 | = | 3 | remainder ( 0 ) | ||||
| GCD = 12 | |||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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