Question
Find Greatest Common Divisor of 420, 560 and 630, using repeated division.
Answer
The GCD of given numbers is 70.
Explanation
Step 1 : Place the numbers inside division bar:.
| 420 | 560 | 630 |
Step 2 : Divide numbers by 2.
| 2 | 420 | 560 | 630 |
| 210 | 280 | 315 |
Step 3 : Divide numbers by 5.
| 2 | 420 | 560 | 630 |
| 5 | 210 | 280 | 315 |
| 42 | 56 | 63 |
Step 4 : Divide numbers by 7.
| 2 | 420 | 560 | 630 |
| 5 | 210 | 280 | 315 |
| 7 | 42 | 56 | 63 |
| 6 | 8 | 9 |
Step 5 : Number 6, 8 and 9, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot5\cdot7 = 70 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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