Question

How can you use number patterns to find the greatest common factor of 120 and 360

Answer 1

Greatest common factor (GCF)

• 120

Finding the factors:

`\begin{gathered} (120)/(2)=60\text{ (2 is a factor)} \\ (60)/(2)=30\text{ (again 2 is a factor)} \\ (30)/(2)=15\text{ (again 2 is a factor)} \\ 15\text{ is not divisible over 2, we search for 3:} \\ (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:} \\ (5)/(5)=1\text{ (5 is another factor, and the last one)} \end{gathered}`

Placing the factors as a multiplication:

`120=2\cdot2\cdot2\cdot3\cdot5`

• 360

`360=2\cdot2\cdot2\cdot3\cdot3\cdot5`

The factors that repeat in each integer are: 2, 2, 2, 3, 5

Therefore, the GFC is:

`\text{GFC}=2\cdot2\cdot2\cdot3\cdot5=120`

Answer: 120