Find Greatest Common Divisor of 96, 144 and 192, using repeated division.

Answer

The GCD of given numbers is 48.

Explanation

Step 1 : Place the numbers inside division bar:.

144

192

Step 2 : Divide numbers by 2.

2	96	144	192
	48	72	96

Step 3 : Divide numbers by 2.

2	96	144	192
2	48	72	96
	24	36	48

Step 4 : Divide numbers by 2.

2	96	144	192
2	48	72	96
2	24	36	48
	12	18	24

Step 5 : Divide numbers by 2.

2	96	144	192
2	48	72	96
2	24	36	48
2	12	18	24
	6	9	12

Step 6 : Divide numbers by 3.

2	96	144	192
2	48	72	96
2	24	36	48
2	12	18	24
3	6	9	12
	2	3	4

Step 7 : Number 2, 3 and 4, cannot be divided any more. The GCD is:

$$ GCD = 2\cdot2\cdot2\cdot2\cdot3 = 48 $$

This solution can be visualized using a Venn diagram.

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

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