Greatest common factor (GCF)
• 120
Finding the factors:
[tex]\begin{gathered} \frac{120}{2}=60\text{ (2 is a factor)} \\ \frac{60}{2}=30\text{ (again 2 is a factor)} \\ \frac{30}{2}=15\text{ (again 2 is a factor)} \\ 15\text{ is not divisible over 2, we search for 3:} \\ \frac{15}{3}=5\text{ (3 is another factor as 15 is divisible over 3)} \\ 5\text{ is not divisible over 2, 3, or 4, we search for 5:} \\ \frac{5}{5}=1\text{ (5 is another factor, and the last one)} \end{gathered}[/tex]Placing the factors as a multiplication:
[tex]120=2\cdot2\cdot2\cdot3\cdot5[/tex]• 360
[tex]360=2\cdot2\cdot2\cdot3\cdot3\cdot5[/tex]The factors that repeat in each integer are: 2, 2, 2, 3, 5
Therefore, the GFC is:
[tex]\text{GFC}=2\cdot2\cdot2\cdot3\cdot5=120[/tex]Answer: 120
