Question
Find Greatest Common Divisor of 60, 75 and 90, using repeated division.
Answer
The GCD of given numbers is 15.
Explanation
Step 1 : Place the numbers inside division bar:.
| 60 | 75 | 90 |
Step 2 : Divide numbers by 3.
| 3 | 60 | 75 | 90 |
| 20 | 25 | 30 |
Step 3 : Divide numbers by 5.
| 3 | 60 | 75 | 90 |
| 5 | 20 | 25 | 30 |
| 4 | 5 | 6 |
Step 4 : Number 4, 5 and 6, cannot be divided any more. The GCD is:
$$ GCD = 3\cdot5 = 15 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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