Find Greatest Common Divisor of 12 and 42, using prime factorization.
Answer
The GCD of given numbers is 6.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}12 =& 2\cdot2\cdot3\\[8pt]42 =& 2\cdot3\cdot7\\[8pt]\end{aligned}$$(view steps on how to factor 12 and 42. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}12 =& \color{blue}{\boxed{2}}\cdot2\cdot\color{red}{\boxed{3}}\\[8pt]42 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{3}}\cdot7\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 2\cdot3 = 6 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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