Find Greatest Common Divisor of 1, 28, 26, 8, 1, 79, 3, 52, 1 and 44, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}1 =& 1~~~ \color{gray}{\text{ (1 is prime)}} \\[8pt]28 =& 2\cdot2\cdot7\\[8pt]26 =& 2\cdot13\\[8pt]8 =& 2\cdot2\cdot2\\[8pt]1 =& 1~~~ \color{gray}{\text{ (1 is prime)}} \\[8pt]79 =& 79\\[8pt]3 =& 3\\[8pt]52 =& 2\cdot2\cdot13\\[8pt]1 =& 1~~~ \color{gray}{\text{ (1 is prime)}} \\[8pt]44 =& 2\cdot2\cdot11\\[8pt]\end{aligned}$$

(view steps on how to factor 1, 28, 26, 8, 1, 79, 3, 52, 1 and 44. )

Step 2 : Put a box around factors that are common for all numbers:

$$\begin{aligned}1 =& 1\\[8pt]28 =& 2\cdot2\cdot7\\[8pt]26 =& 2\cdot13\\[8pt]8 =& 2\cdot2\cdot2\\[8pt]1 =& 1\\[8pt]79 =& 79\\[8pt]3 =& 3\\[8pt]52 =& 2\cdot2\cdot13\\[8pt]1 =& 1\\[8pt]44 =& 2\cdot2\cdot11\\[8pt]\end{aligned}$$

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} } $.

GCD Calculator