Find Greatest Common Divisor of 2300 and 1180, using repeated division.
Answer
The GCD of given numbers is 20.
Explanation
Step 1 : Place the numbers inside division bar:.
| 2300 | 1180 |
Step 2 : Divide numbers by 2.
| 2 | 2300 | 1180 |
| 1150 | 590 |
Step 3 : Divide numbers by 2.
| 2 | 2300 | 1180 |
| 2 | 1150 | 590 |
| 575 | 295 |
Step 4 : Divide numbers by 5.
| 2 | 2300 | 1180 |
| 2 | 1150 | 590 |
| 5 | 575 | 295 |
| 115 | 59 |
Step 5 : Number 115 and 59, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot2\cdot5 = 20 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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