Find Greatest Common Divisor of 13, 16, 31, 34 and 43, using prime factorization.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}13 =& 13\\[8pt]16 =& 2\cdot2\cdot2\cdot2\\[8pt]31 =& 31\\[8pt]34 =& 2\cdot17\\[8pt]43 =& 43\\[8pt]\end{aligned}$$(view steps on how to factor 13, 16, 31, 34 and 43. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}13 =& 13\\[8pt]16 =& 2\cdot2\cdot2\cdot2\\[8pt]31 =& 31\\[8pt]34 =& 2\cdot17\\[8pt]43 =& 43\\[8pt]\end{aligned}$$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