Question
Find Greatest Common Divisor of 105 and 840, using repeated division.
Answer
The GCD of given numbers is 105.
Explanation
Step 1 : Place the numbers inside division bar:.
| 105 | 840 |
Step 2 : Divide numbers by 3.
| 3 | 105 | 840 |
| 35 | 280 |
Step 3 : Divide numbers by 5.
| 3 | 105 | 840 |
| 5 | 35 | 280 |
| 7 | 56 |
Step 4 : Divide numbers by 7.
| 3 | 105 | 840 |
| 5 | 35 | 280 |
| 7 | 7 | 56 |
| 1 | 8 |
Step 5 : Number 1 and 8, cannot be divided any more. The GCD is:
$$ GCD = 3\cdot5\cdot7 = 105 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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