Find Greatest Common Divisor of 576, 672 and 1632, using repeated division.

Answer

The GCD of given numbers is 96.

Explanation

Step 1 : Place the numbers inside division bar:.

576

672

1632

Step 2 : Divide numbers by 2.

2	576	672	1632
	288	336	816

Step 3 : Divide numbers by 2.

2	576	672	1632
2	288	336	816
	144	168	408

Step 4 : Divide numbers by 2.

2	576	672	1632
2	288	336	816
2	144	168	408
	72	84	204

Step 5 : Divide numbers by 2.

2	576	672	1632
2	288	336	816
2	144	168	408
2	72	84	204
	36	42	102

Step 6 : Divide numbers by 2.

2	576	672	1632
2	288	336	816
2	144	168	408
2	72	84	204
2	36	42	102
	18	21	51

Step 7 : Divide numbers by 3.

2	576	672	1632
2	288	336	816
2	144	168	408
2	72	84	204
2	36	42	102
3	18	21	51
	6	7	17

Step 8 : Number 6, 7 and 17, cannot be divided any more. The GCD is:

$$ GCD = 2\cdot2\cdot2\cdot2\cdot2\cdot3 = 96 $$

This solution can be visualized using a Venn diagram.

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

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