Find Greatest Common Divisor of 10, 14 and 22, using prime factorization.
Answer
The GCD of given numbers is 2.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}10 =& 2\cdot5\\[8pt]14 =& 2\cdot7\\[8pt]22 =& 2\cdot11\\[8pt]\end{aligned}$$(view steps on how to factor 10, 14 and 22. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}10 =& \color{blue}{\boxed{2}}\cdot5\\[8pt]14 =& \color{blue}{\boxed{2}}\cdot7\\[8pt]22 =& \color{blue}{\boxed{2}}\cdot11\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 2 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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