Question
Find Greatest Common Divisor of 220 and 440, using repeated division.
Answer
The GCD of given numbers is 220.
Explanation
Step 1 : Place the numbers inside division bar:.
| 220 | 440 |
Step 2 : Divide numbers by 2.
| 2 | 220 | 440 |
| 110 | 220 |
Step 3 : Divide numbers by 2.
| 2 | 220 | 440 |
| 2 | 110 | 220 |
| 55 | 110 |
Step 4 : Divide numbers by 5.
| 2 | 220 | 440 |
| 2 | 110 | 220 |
| 5 | 55 | 110 |
| 11 | 22 |
Step 5 : Divide numbers by 11.
| 2 | 220 | 440 |
| 2 | 110 | 220 |
| 5 | 55 | 110 |
| 11 | 11 | 22 |
| 1 | 2 |
Step 6 : Number 1 and 2, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot2\cdot5\cdot11 = 220 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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