Find Greatest Common Divisor of 1344, 1856 and 2752, using repeated division.

Answer

The GCD of given numbers is 64.

Explanation

Step 1 : Place the numbers inside division bar:.

1344

1856

2752

Step 2 : Divide numbers by 2.

2	1344	1856	2752
	672	928	1376

Step 3 : Divide numbers by 2.

2	1344	1856	2752
2	672	928	1376
	336	464	688

Step 4 : Divide numbers by 2.

2	1344	1856	2752
2	672	928	1376
2	336	464	688
	168	232	344

Step 5 : Divide numbers by 2.

2	1344	1856	2752
2	672	928	1376
2	336	464	688
2	168	232	344
	84	116	172

Step 6 : Divide numbers by 2.

2	1344	1856	2752
2	672	928	1376
2	336	464	688
2	168	232	344
2	84	116	172
	42	58	86

Step 7 : Divide numbers by 2.

2	1344	1856	2752
2	672	928	1376
2	336	464	688
2	168	232	344
2	84	116	172
2	42	58	86
	21	29	43

Step 8 : Number 21, 29 and 43, cannot be divided any more. The GCD is:

$$ GCD = 2\cdot2\cdot2\cdot2\cdot2\cdot2 = 64 $$

This solution can be visualized using a Venn diagram.

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

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