Find Greatest Common Divisor of 12, 14, 34, 41, 47 and 34, using prime factorization.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}12 =& 2\cdot2\cdot3\\[8pt]14 =& 2\cdot7\\[8pt]34 =& 2\cdot17\\[8pt]41 =& 41\\[8pt]47 =& 47\\[8pt]34 =& 2\cdot17\\[8pt]\end{aligned}$$(view steps on how to factor 12, 14, 34, 41, 47 and 34. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}12 =& 2\cdot2\cdot3\\[8pt]14 =& 2\cdot7\\[8pt]34 =& 2\cdot17\\[8pt]41 =& 41\\[8pt]47 =& 47\\[8pt]34 =& 2\cdot17\\[8pt]\end{aligned}$$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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