Question
Find Greatest Common Divisor of 108, 288 and 360, using repeated division.
Answer
The GCD of given numbers is 36.
Explanation
Step 1 : Place the numbers inside division bar:.
| 108 | 288 | 360 |
Step 2 : Divide numbers by 2.
| 2 | 108 | 288 | 360 |
| 54 | 144 | 180 |
Step 3 : Divide numbers by 2.
| 2 | 108 | 288 | 360 |
| 2 | 54 | 144 | 180 |
| 27 | 72 | 90 |
Step 4 : Divide numbers by 3.
| 2 | 108 | 288 | 360 |
| 2 | 54 | 144 | 180 |
| 3 | 27 | 72 | 90 |
| 9 | 24 | 30 |
Step 5 : Divide numbers by 3.
| 2 | 108 | 288 | 360 |
| 2 | 54 | 144 | 180 |
| 3 | 27 | 72 | 90 |
| 3 | 9 | 24 | 30 |
| 3 | 8 | 10 |
Step 6 : Number 3, 8 and 10, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot2\cdot3\cdot3 = 36 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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