Find Greatest Common Divisor of 400 and 60, using Euclidean algorithm.
Answer
The GCD of given numbers is 20.
Explanation
Step 1 :
Divide $ 400 $ by $ 60 $ and get the remainder
The remainder is positive ($ 40 > 0 $), so we will continue with division.
Step 2 :
Divide $ 60 $ by $ \color{blue}{ 40 } $ and get the remainder
The remainder is still positive ($ 20 > 0 $), so we will continue with division.
Step 3 :
Divide $ 40 $ by $ \color{blue}{ 20 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 20 }} $.
We can summarize an algorithm into a following table.
| 400 | : | 60 | = | 6 | remainder ( 40 ) | ||||
| 60 | : | 40 | = | 1 | remainder ( 20 ) | ||||
| 40 | : | 20 | = | 2 | remainder ( 0 ) | ||||
| GCD = 20 | |||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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