Find Greatest Common Divisor of 117, 91 and 65, using prime factorization.
Answer
The GCD of given numbers is 13.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}117 =& 3\cdot3\cdot13\\[8pt]91 =& 7\cdot13\\[8pt]65 =& 5\cdot13\\[8pt]\end{aligned}$$(view steps on how to factor 117, 91 and 65. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}117 =& 3\cdot3\cdot\color{blue}{\boxed{13}}\\[8pt]91 =& 7\cdot\color{blue}{\boxed{13}}\\[8pt]65 =& 5\cdot\color{blue}{\boxed{13}}\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 13 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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