Find Greatest Common Divisor of 1755 and 2475, using repeated division.
Answer
The GCD of given numbers is 45.
Explanation
Step 1 : Place the numbers inside division bar:.
| 1755 | 2475 |
Step 2 : Divide numbers by 3.
| 3 | 1755 | 2475 |
| 585 | 825 |
Step 3 : Divide numbers by 3.
| 3 | 1755 | 2475 |
| 3 | 585 | 825 |
| 195 | 275 |
Step 4 : Divide numbers by 5.
| 3 | 1755 | 2475 |
| 3 | 585 | 825 |
| 5 | 195 | 275 |
| 39 | 55 |
Step 5 : Number 39 and 55, cannot be divided any more. The GCD is:
$$ GCD = 3\cdot3\cdot5 = 45 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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