Question
Find Greatest Common Divisor of 6499 and 4288, using prime factorization.
Answer
The GCD of given numbers is 67.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}6499 =& 67\cdot97\\[8pt]4288 =& 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot67\\[8pt]\end{aligned}$$(view steps on how to factor 6499 and 4288. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}6499 =& \color{blue}{\boxed{67}}\cdot97\\[8pt]4288 =& 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot\color{blue}{\boxed{67}}\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 67 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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