Find Greatest Common Divisor of 245 and 112, using Euclidean algorithm.
Answer
The GCD of given numbers is 7.
Explanation
Step 1 :
Divide $ 245 $ by $ 112 $ and get the remainder
The remainder is positive ($ 21 > 0 $), so we will continue with division.
Step 2 :
Divide $ 112 $ by $ \color{blue}{ 21 } $ and get the remainder
The remainder is still positive ($ 7 > 0 $), so we will continue with division.
Step 3 :
Divide $ 21 $ by $ \color{blue}{ 7 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 7 }} $.
We can summarize an algorithm into a following table.
| 245 | : | 112 | = | 2 | remainder ( 21 ) | ||||
| 112 | : | 21 | = | 5 | remainder ( 7 ) | ||||
| 21 | : | 7 | = | 3 | remainder ( 0 ) | ||||
| GCD = 7 | |||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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