Question
Find Greatest Common Divisor of 1003 and 2006, using prime factorization.
Answer
The GCD of given numbers is 1003.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}1003 =& 17\cdot59\\[8pt]2006 =& 2\cdot17\cdot59\\[8pt]\end{aligned}$$(view steps on how to factor 1003 and 2006. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}1003 =& \color{blue}{\boxed{17}}\cdot\color{red}{\boxed{59}}\\[8pt]2006 =& 2\cdot\color{blue}{\boxed{17}}\cdot\color{red}{\boxed{59}}\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 17\cdot59 = 1003 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
This page was created using
GCD Calculator