Find Greatest Common Divisor of 144, 216 and 360, using repeated division.

Answer

The GCD of given numbers is 72.

Explanation

Step 1 : Place the numbers inside division bar:.

144

216

360

Step 2 : Divide numbers by 2.

2	144	216	360
	72	108	180

Step 3 : Divide numbers by 2.

2	144	216	360
2	72	108	180
	36	54	90

Step 4 : Divide numbers by 2.

2	144	216	360
2	72	108	180
2	36	54	90
	18	27	45

Step 5 : Divide numbers by 3.

2	144	216	360
2	72	108	180
2	36	54	90
3	18	27	45
	6	9	15

Step 6 : Divide numbers by 3.

2	144	216	360
2	72	108	180
2	36	54	90
3	18	27	45
3	6	9	15
	2	3	5

Step 7 : Number 2, 3 and 5, cannot be divided any more. The GCD is:

$$ GCD = 2\cdot2\cdot2\cdot3\cdot3 = 72 $$

This solution can be visualized using a Venn diagram.

The GCD equals the product of the numbers at the intersection.

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