Question
Find Greatest Common Divisor of 60 and 120, using repeated division.
Answer
The GCD of given numbers is 60.
Explanation
Step 1 : Place the numbers inside division bar:.
| 60 | 120 |
Step 2 : Divide numbers by 2.
| 2 | 60 | 120 |
| 30 | 60 |
Step 3 : Divide numbers by 2.
| 2 | 60 | 120 |
| 2 | 30 | 60 |
| 15 | 30 |
Step 4 : Divide numbers by 3.
| 2 | 60 | 120 |
| 2 | 30 | 60 |
| 3 | 15 | 30 |
| 5 | 10 |
Step 5 : Divide numbers by 5.
| 2 | 60 | 120 |
| 2 | 30 | 60 |
| 3 | 15 | 30 |
| 5 | 5 | 10 |
| 1 | 2 |
Step 6 : Number 1 and 2, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot2\cdot3\cdot5 = 60 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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