Question
Find Greatest Common Divisor of 10, 20, 6 and 30, using prime factorization.
Answer
The GCD of given numbers is 2.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}10 =& 2\cdot5\\[8pt]20 =& 2\cdot2\cdot5\\[8pt]6 =& 2\cdot3\\[8pt]30 =& 2\cdot3\cdot5\\[8pt]\end{aligned}$$(view steps on how to factor 10, 20, 6 and 30. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}10 =& \color{blue}{\boxed{2}}\cdot5\\[8pt]20 =& \color{blue}{\boxed{2}}\cdot2\cdot5\\[8pt]6 =& \color{blue}{\boxed{2}}\cdot3\\[8pt]30 =& \color{blue}{\boxed{2}}\cdot3\cdot5\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 2 $$This page was created using
GCD Calculator