Question
Find Greatest Common Divisor of 150, 360 and 900, using repeated division.
Answer
The GCD of given numbers is 30.
Explanation
Step 1 : Place the numbers inside division bar:.
| 150 | 360 | 900 |
Step 2 : Divide numbers by 2.
| 2 | 150 | 360 | 900 |
| 75 | 180 | 450 |
Step 3 : Divide numbers by 3.
| 2 | 150 | 360 | 900 |
| 3 | 75 | 180 | 450 |
| 25 | 60 | 150 |
Step 4 : Divide numbers by 5.
| 2 | 150 | 360 | 900 |
| 3 | 75 | 180 | 450 |
| 5 | 25 | 60 | 150 |
| 5 | 12 | 30 |
Step 5 : Number 5, 12 and 30, 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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