Find Greatest Common Divisor of 512 and 384, using repeated division.

Answer

The GCD of given numbers is 128.

Explanation

Step 1 : Place the numbers inside division bar:.

512

384

Step 2 : Divide numbers by 2.

2	512	384
	256	192

Step 3 : Divide numbers by 2.

2	512	384
2	256	192
	128	96

Step 4 : Divide numbers by 2.

2	512	384
2	256	192
2	128	96
	64	48

Step 5 : Divide numbers by 2.

2	512	384
2	256	192
2	128	96
2	64	48
	32	24

Step 6 : Divide numbers by 2.

2	512	384
2	256	192
2	128	96
2	64	48
2	32	24
	16	12

Step 7 : Divide numbers by 2.

2	512	384
2	256	192
2	128	96
2	64	48
2	32	24
2	16	12
	8	6

Step 8 : Divide numbers by 2.

2	512	384
2	256	192
2	128	96
2	64	48
2	32	24
2	16	12
2	8	6
	4	3

Step 9 : Number 4 and 3, cannot be divided any more. The GCD is:

$$ GCD = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2 = 128 $$

This solution can be visualized using a Venn diagram.

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

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