Question
Find Greatest Common Divisor of 154 and 198, using prime factorization.
Answer
The GCD of given numbers is 22.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}154 =& 2\cdot7\cdot11\\[8pt]198 =& 2\cdot3\cdot3\cdot11\\[8pt]\end{aligned}$$(view steps on how to factor 154 and 198. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}154 =& \color{blue}{\boxed{2}}\cdot7\cdot\color{red}{\boxed{11}}\\[8pt]198 =& \color{blue}{\boxed{2}}\cdot3\cdot3\cdot\color{red}{\boxed{11}}\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 2\cdot11 = 22 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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