Question
Find Greatest Common Divisor of 90, 60 and 30, using repeated division.
Answer
The GCD of given numbers is 30.
Explanation
Step 1 : Place the numbers inside division bar:.
| 90 | 60 | 30 |
Step 2 : Divide numbers by 2.
| 2 | 90 | 60 | 30 |
| 45 | 30 | 15 |
Step 3 : Divide numbers by 3.
| 2 | 90 | 60 | 30 |
| 3 | 45 | 30 | 15 |
| 15 | 10 | 5 |
Step 4 : Divide numbers by 5.
| 2 | 90 | 60 | 30 |
| 3 | 45 | 30 | 15 |
| 5 | 15 | 10 | 5 |
| 3 | 2 | 1 |
Step 5 : Number 3, 2 and 1, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot3\cdot5 = 30 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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