Question
Find Greatest Common Divisor of 5264 and 15472, using repeated division.
Answer
The GCD of given numbers is 16.
Explanation
Step 1 : Place the numbers inside division bar:.
| 5264 | 15472 |
Step 2 : Divide numbers by 2.
| 2 | 5264 | 15472 |
| 2632 | 7736 |
Step 3 : Divide numbers by 2.
| 2 | 5264 | 15472 |
| 2 | 2632 | 7736 |
| 1316 | 3868 |
Step 4 : Divide numbers by 2.
| 2 | 5264 | 15472 |
| 2 | 2632 | 7736 |
| 2 | 1316 | 3868 |
| 658 | 1934 |
Step 5 : Divide numbers by 2.
| 2 | 5264 | 15472 |
| 2 | 2632 | 7736 |
| 2 | 1316 | 3868 |
| 2 | 658 | 1934 |
| 329 | 967 |
Step 6 : Number 329 and 967, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot2\cdot2\cdot2 = 16 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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