Find Greatest Common Divisor of 2, 3, 33, 39, 41 and 7, using prime factorization.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}2 =& 2\\[8pt]3 =& 3\\[8pt]33 =& 3\cdot11\\[8pt]39 =& 3\cdot13\\[8pt]41 =& 41\\[8pt]7 =& 7\\[8pt]\end{aligned}$$(view steps on how to factor 2, 3, 33, 39, 41 and 7. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}2 =& 2\\[8pt]3 =& 3\\[8pt]33 =& 3\cdot11\\[8pt]39 =& 3\cdot13\\[8pt]41 =& 41\\[8pt]7 =& 7\\[8pt]\end{aligned}$$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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