Find Greatest Common Divisor of 1260 and 10500, using Euclidean algorithm.
Answer
The GCD of given numbers is 420.
Explanation
Step 1 :
Divide $ 10500 $ by $ 1260 $ and get the remainder
The remainder is positive ($ 420 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1260 $ by $ \color{blue}{ 420 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 420 }} $.
We can summarize an algorithm into a following table.
| 10500 | : | 1260 | = | 8 | remainder ( 420 ) | ||
| 1260 | : | 420 | = | 3 | remainder ( 0 ) | ||
| GCD = 420 | |||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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