Question
Find Greatest Common Divisor of 252 and 105, using Euclidean algorithm.
Answer
The GCD of given numbers is 21.
Explanation
Step 1 :
Divide by and get the remainder
The remainder is positive (), so we will continue with division.
Step 2 :
Divide by and get the remainder
The remainder is still positive (), so we will continue with division.
Step 3 :
Divide by and get the remainder
The remainder is zero => GCD is the last divisor .
We can summarize an algorithm into a following table.
| 252 | : | 105 | = | 2 | remainder ( 42 ) | ||||
| 105 | : | 42 | = | 2 | remainder ( 21 ) | ||||
| 42 | : | 21 | = | 2 | remainder ( 0 ) | ||||
| GCD = 21 | |||||||||
This solution can be visualized using a Venn diagram.
0,0
252
105
3
7
2
2
3
5
The GCD equals the product of the numbers at the intersection.
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