Question
Find Greatest Common Divisor of 22086 and 9990, using repeated division.
Answer
The GCD of given numbers is 54.
Explanation
Step 1 : Place the numbers inside division bar:.
| 22086 | 9990 |
Step 2 : Divide numbers by 2.
| 2 | 22086 | 9990 |
| 11043 | 4995 |
Step 3 : Divide numbers by 3.
| 2 | 22086 | 9990 |
| 3 | 11043 | 4995 |
| 3681 | 1665 |
Step 4 : Divide numbers by 3.
| 2 | 22086 | 9990 |
| 3 | 11043 | 4995 |
| 3 | 3681 | 1665 |
| 1227 | 555 |
Step 5 : Divide numbers by 3.
| 2 | 22086 | 9990 |
| 3 | 11043 | 4995 |
| 3 | 3681 | 1665 |
| 3 | 1227 | 555 |
| 409 | 185 |
Step 6 : Number 409 and 185, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot3\cdot3\cdot3 = 54 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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