Question
Find Greatest Common Divisor of 17 and 969, using prime factorization.
Answer
The GCD of given numbers is 17.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}17 =& 17\\[8pt]969 =& 3\cdot17\cdot19\\[8pt]\end{aligned}$$(view steps on how to factor 17 and 969. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}17 =& \color{blue}{\boxed{17}}\\[8pt]969 =& 3\cdot\color{blue}{\boxed{17}}\cdot19\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 17 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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