Find Greatest Common Divisor of 314 and 520, using prime factorization.
Answer
The GCD of given numbers is 2.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}314 =& 2\cdot157\\[8pt]520 =& 2\cdot2\cdot2\cdot5\cdot13\\[8pt]\end{aligned}$$(view steps on how to factor 314 and 520. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}314 =& \color{blue}{\boxed{2}}\cdot157\\[8pt]520 =& \color{blue}{\boxed{2}}\cdot2\cdot2\cdot5\cdot13\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 2 $$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