Question
Find Greatest Common Divisor of 452 and 6004, using prime factorization.
Answer
The GCD of given numbers is 4.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}452 =& 2\cdot2\cdot113\\[8pt]6004 =& 2\cdot2\cdot19\cdot79\\[8pt]\end{aligned}$$(view steps on how to factor 452 and 6004. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}452 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot113\\[8pt]6004 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot19\cdot79\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 2\cdot2 = 4 $$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