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

User Sargunv
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1 Answer

20 votes
20 votes

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

User Adam Ware
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