Question
Find Greatest Common Divisor of 1003 and 708, using prime factorization.
Answer
The GCD of given numbers is 59.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}1003 =& 17\cdot59\\[8pt]708 =& 2\cdot2\cdot3\cdot59\\[8pt]\end{aligned}$$(view steps on how to factor 1003 and 708. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}1003 =& 17\cdot\color{blue}{\boxed{59}}\\[8pt]708 =& 2\cdot2\cdot3\cdot\color{blue}{\boxed{59}}\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 59 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
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