Question
Find Greatest Common Divisor of 210 and 42, using repeated division.
Answer
The GCD of given numbers is 42.
Explanation
Step 1 : Place the numbers inside division bar:.
| 210 | 42 |
Step 2 : Divide numbers by 2.
| 2 | 210 | 42 |
| 105 | 21 |
Step 3 : Divide numbers by 3.
| 2 | 210 | 42 |
| 3 | 105 | 21 |
| 35 | 7 |
Step 4 : Divide numbers by 7.
| 2 | 210 | 42 |
| 3 | 105 | 21 |
| 7 | 35 | 7 |
| 5 | 1 |
Step 5 : Number 5 and 1, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot3\cdot7 = 42 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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