Question
Find Greatest Common Divisor of 168, 420 and 588, using repeated division.
Answer
The GCD of given numbers is 12.
Explanation
Step 1 : Place the numbers inside division bar:.
| 168 | 420 | 588 |
Step 2 : Divide numbers by 2.
| 2 | 168 | 420 | 588 |
| 84 | 210 | 294 |
Step 3 : Divide numbers by 2.
| 2 | 168 | 420 | 588 |
| 2 | 84 | 210 | 294 |
| 42 | 105 | 147 |
Step 4 : Divide numbers by 3.
| 2 | 168 | 420 | 588 |
| 2 | 84 | 210 | 294 |
| 3 | 42 | 105 | 147 |
| 14 | 35 | 49 |
Step 5 : Number 14, 35 and 49, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot2\cdot3 = 12 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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