The GCD of given numbers is 36.
Step 1 : Place the numbers inside division bar:.
108 | 144 |
Step 2 : Divide numbers by 2.
2 | 108 | 144 |
54 | 72 |
Step 3 : Divide numbers by 2.
2 | 108 | 144 |
2 | 54 | 72 |
27 | 36 |
Step 4 : Divide numbers by 3.
2 | 108 | 144 |
2 | 54 | 72 |
3 | 27 | 36 |
9 | 12 |
Step 5 : Divide numbers by 3.
2 | 108 | 144 |
2 | 54 | 72 |
3 | 27 | 36 |
3 | 9 | 12 |
3 | 4 |
Step 6 : Number 3 and 4, cannot be divided any more. The GCD is:
$$ GCD = 2\cdot2\cdot3\cdot3 = 36 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.