Find Greatest Common Divisor of 6, 11, 17, 22, 28, 33, 38, 44, 49 and 55, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}6 =& 2\cdot3\\[8pt]11 =& 11\\[8pt]17 =& 17\\[8pt]22 =& 2\cdot11\\[8pt]28 =& 2\cdot2\cdot7\\[8pt]33 =& 3\cdot11\\[8pt]38 =& 2\cdot19\\[8pt]44 =& 2\cdot2\cdot11\\[8pt]49 =& 7\cdot7\\[8pt]55 =& 5\cdot11\\[8pt]\end{aligned}$$

(view steps on how to factor 6, 11, 17, 22, 28, 33, 38, 44, 49 and 55. )

Step 2 : Put a box around factors that are common for all numbers:

$$\begin{aligned}6 =& 2\cdot3\\[8pt]11 =& 11\\[8pt]17 =& 17\\[8pt]22 =& 2\cdot11\\[8pt]28 =& 2\cdot2\cdot7\\[8pt]33 =& 3\cdot11\\[8pt]38 =& 2\cdot19\\[8pt]44 =& 2\cdot2\cdot11\\[8pt]49 =& 7\cdot7\\[8pt]55 =& 5\cdot11\\[8pt]\end{aligned}$$

Note that in this example numbers do not have any common factors.

Step 3 : Multiply the boxed numbers together:

Since there is no boxed numbers we conclude that $~\color{blue}{ \text{GCD = 1} } $.

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