Find Greatest Common Divisor of 1330 and 42, using Euclidean algorithm.
Answer
The GCD of given numbers is 14.
Explanation
Step 1 :
Divide $ 1330 $ by $ 42 $ and get the remainder
The remainder is positive ($ 28 > 0 $), so we will continue with division.
Step 2 :
Divide $ 42 $ by $ \color{blue}{ 28 } $ and get the remainder
The remainder is still positive ($ 14 > 0 $), so we will continue with division.
Step 3 :
Divide $ 28 $ by $ \color{blue}{ 14 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 14 }} $.
We can summarize an algorithm into a following table.
| 1330 | : | 42 | = | 31 | remainder ( 28 ) | ||||
| 42 | : | 28 | = | 1 | remainder ( 14 ) | ||||
| 28 | : | 14 | = | 2 | remainder ( 0 ) | ||||
| GCD = 14 | |||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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