Find Greatest Common Divisor of 630 and 1260, using repeated division.
Answer
The GCD of given numbers is 630.
Explanation
Step 1 : Place the numbers inside division bar:.
| 630 | 1260 |
Step 2 : Divide numbers by 2.
| 2 | 630 | 1260 |
| 315 | 630 |
Step 3 : Divide numbers by 3.
| 2 | 630 | 1260 |
| 3 | 315 | 630 |
| 105 | 210 |
Step 4 : Divide numbers by 3.
| 2 | 630 | 1260 |
| 3 | 315 | 630 |
| 3 | 105 | 210 |
| 35 | 70 |
Step 5 : Divide numbers by 5.
| 2 | 630 | 1260 |
| 3 | 315 | 630 |
| 3 | 105 | 210 |
| 5 | 35 | 70 |
| 7 | 14 |
Step 6 : Divide numbers by 7.
| 2 | 630 | 1260 |
| 3 | 315 | 630 |
| 3 | 105 | 210 |
| 5 | 35 | 70 |
| 7 | 7 | 14 |
| 1 | 2 |
Step 7 : Number 1 and 2, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot3\cdot3\cdot5\cdot7 = 630 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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