Question
Find Greatest Common Divisor of 60, 132 and 168, using repeated division.
Answer
The GCD of given numbers is 12.
Explanation
Step 1 : Place the numbers inside division bar:.
| 60 | 132 | 168 |
Step 2 : Divide numbers by 2.
| 2 | 60 | 132 | 168 |
| 30 | 66 | 84 |
Step 3 : Divide numbers by 2.
| 2 | 60 | 132 | 168 |
| 2 | 30 | 66 | 84 |
| 15 | 33 | 42 |
Step 4 : Divide numbers by 3.
| 2 | 60 | 132 | 168 |
| 2 | 30 | 66 | 84 |
| 3 | 15 | 33 | 42 |
| 5 | 11 | 14 |
Step 5 : Number 5, 11 and 14, 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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