Question
Find Greatest Common Divisor of 875 and 1000, using repeated division.
Answer
The GCD of given numbers is 125.
Explanation
Step 1 : Place the numbers inside division bar:.
| 875 | 1000 |
Step 2 : Divide numbers by 5.
| 5 | 875 | 1000 |
| 175 | 200 |
Step 3 : Divide numbers by 5.
| 5 | 875 | 1000 |
| 5 | 175 | 200 |
| 35 | 40 |
Step 4 : Divide numbers by 5.
| 5 | 875 | 1000 |
| 5 | 175 | 200 |
| 5 | 35 | 40 |
| 7 | 8 |
Step 5 : Number 7 and 8, cannot be divided any more. The GCD is:
$$ GCD = 5\cdot5\cdot5 = 125 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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