Find Greatest Common Divisor of 27, 80, 108, 20 and 75, using prime factorization.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}27 =& 3\cdot3\cdot3\\[8pt]80 =& 2\cdot2\cdot2\cdot2\cdot5\\[8pt]108 =& 2\cdot2\cdot3\cdot3\cdot3\\[8pt]20 =& 2\cdot2\cdot5\\[8pt]75 =& 3\cdot5\cdot5\\[8pt]\end{aligned}$$(view steps on how to factor 27, 80, 108, 20 and 75. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}27 =& 3\cdot3\cdot3\\[8pt]80 =& 2\cdot2\cdot2\cdot2\cdot5\\[8pt]108 =& 2\cdot2\cdot3\cdot3\cdot3\\[8pt]20 =& 2\cdot2\cdot5\\[8pt]75 =& 3\cdot5\cdot5\\[8pt]\end{aligned}$$Note that in this example numbers do not have any common factors.
Step 3 : Multiply the boxed numbers together:
Since there is no boxed numbers we conclude that $~\color{blue}{ \text{GCD = 1} } $.
This page was created using
GCD Calculator