Question
Find Greatest Common Divisor of 850 and 1000, using repeated division.
Answer
The GCD of given numbers is 50.
Explanation
Step 1 : Place the numbers inside division bar:.
| 850 | 1000 |
Step 2 : Divide numbers by 2.
| 2 | 850 | 1000 |
| 425 | 500 |
Step 3 : Divide numbers by 5.
| 2 | 850 | 1000 |
| 5 | 425 | 500 |
| 85 | 100 |
Step 4 : Divide numbers by 5.
| 2 | 850 | 1000 |
| 5 | 425 | 500 |
| 5 | 85 | 100 |
| 17 | 20 |
Step 5 : Number 17 and 20, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot5\cdot5 = 50 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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