Question
Find Greatest Common Divisor of 240, 280 and 560, using repeated division.
Answer
The GCD of given numbers is 40.
Explanation
Step 1 : Place the numbers inside division bar:.
| 240 | 280 | 560 |
Step 2 : Divide numbers by 2.
| 2 | 240 | 280 | 560 |
| 120 | 140 | 280 |
Step 3 : Divide numbers by 2.
| 2 | 240 | 280 | 560 |
| 2 | 120 | 140 | 280 |
| 60 | 70 | 140 |
Step 4 : Divide numbers by 2.
| 2 | 240 | 280 | 560 |
| 2 | 120 | 140 | 280 |
| 2 | 60 | 70 | 140 |
| 30 | 35 | 70 |
Step 5 : Divide numbers by 5.
| 2 | 240 | 280 | 560 |
| 2 | 120 | 140 | 280 |
| 2 | 60 | 70 | 140 |
| 5 | 30 | 35 | 70 |
| 6 | 7 | 14 |
Step 6 : Number 6, 7 and 14, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot2\cdot2\cdot5 = 40 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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