Find Greatest Common Divisor of 144, 1008 and 432, using repeated division.

Answer

The GCD of given numbers is 144.

Explanation

Step 1 : Place the numbers inside division bar:.

144

1008

432

Step 2 : Divide numbers by 2.

2	144	1008	432
	72	504	216

Step 3 : Divide numbers by 2.

2	144	1008	432
2	72	504	216
	36	252	108

Step 4 : Divide numbers by 2.

2	144	1008	432
2	72	504	216
2	36	252	108
	18	126	54

Step 5 : Divide numbers by 2.

2	144	1008	432
2	72	504	216
2	36	252	108
2	18	126	54
	9	63	27

Step 6 : Divide numbers by 3.

2	144	1008	432
2	72	504	216
2	36	252	108
2	18	126	54
3	9	63	27
	3	21	9

Step 7 : Divide numbers by 3.

2	144	1008	432
2	72	504	216
2	36	252	108
2	18	126	54
3	9	63	27
3	3	21	9
	1	7	3

Step 8 : Number 1, 7 and 3, cannot be divided any more. The GCD is:

$$ GCD = 2\cdot2\cdot2\cdot2\cdot3\cdot3 = 144 $$

This solution can be visualized using a Venn diagram.

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

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