Find Greatest Common Divisor of 123 and 456, using prime factorization.
Answer
The GCD of given numbers is 3.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}123 =& 3\cdot41\\[8pt]456 =& 2\cdot2\cdot2\cdot3\cdot19\\[8pt]\end{aligned}$$(view steps on how to factor 123 and 456. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}123 =& \color{blue}{\boxed{3}}\cdot41\\[8pt]456 =& 2\cdot2\cdot2\cdot\color{blue}{\boxed{3}}\cdot19\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 3 $$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