Question
Find Greatest Common Divisor of 1512 and 3780, using repeated division.
Answer
The GCD of given numbers is 108.
Explanation
Step 1 : Place the numbers inside division bar:.
| 1512 | 3780 |
Step 2 : Divide numbers by 2.
| 2 | 1512 | 3780 |
| 756 | 1890 |
Step 3 : Divide numbers by 2.
| 2 | 1512 | 3780 |
| 2 | 756 | 1890 |
| 378 | 945 |
Step 4 : Divide numbers by 3.
| 2 | 1512 | 3780 |
| 2 | 756 | 1890 |
| 3 | 378 | 945 |
| 126 | 315 |
Step 5 : Divide numbers by 3.
| 2 | 1512 | 3780 |
| 2 | 756 | 1890 |
| 3 | 378 | 945 |
| 3 | 126 | 315 |
| 42 | 105 |
Step 6 : Divide numbers by 3.
| 2 | 1512 | 3780 |
| 2 | 756 | 1890 |
| 3 | 378 | 945 |
| 3 | 126 | 315 |
| 3 | 42 | 105 |
| 14 | 35 |
Step 7 : Number 14 and 35, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot2\cdot3\cdot3\cdot3 = 108 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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