gcf of 120

Guri Bee

2 min read

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22-10-2024

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Unlocking the Greatest Common Factor: A Deep Dive into 120

The Greatest Common Factor (GCF) of a set of numbers is the largest number that divides into all of them evenly. Let's explore the GCF of 120, a number that holds a surprising amount of factors.

1. Understanding the Problem

We want to find the largest number that divides both 120 and itself without leaving a remainder. To do this, we can use a few different methods:

2. Prime Factorization Method

This method breaks down each number into its prime factors, the smallest numbers that multiply to create it. Here's how it works for 120:

• 120: 2 x 2 x 2 x 3 x 5

Now, we identify the common prime factors and their lowest powers:

• Common Factors: 2 x 2 x 3 x 5

Finally, we multiply these common factors to find the GCF:

• GCF(120) = 2 x 2 x 3 x 5 = 60

3. Listing Factors Method

This approach involves listing all the factors of 120 and then finding the largest common factor.

• Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

The largest number that divides into 120 and itself is 60.

4. Applications of GCF

Finding the GCF has practical applications beyond just understanding divisibility:

• Simplifying Fractions: GCF can help reduce fractions to their simplest form. For example, 60/120 can be simplified to 1/2 by dividing both numerator and denominator by their GCF, 60.
• Dividing Objects into Equal Groups: The GCF helps determine the largest possible group size when dividing objects evenly. If you have 120 marbles and want to divide them into equal groups, the GCF (60) tells you the largest group size possible.

5. Additional Insights

• The GCF of a number and itself is always that number.
• The GCF of a number and 1 is always 1.
• The GCF of two numbers is always less than or equal to the smaller of the two numbers.

Conclusion

Finding the GCF of 120 might seem like a simple exercise, but it opens the door to understanding fundamental concepts in mathematics. From simplifying fractions to dividing objects into equal groups, the GCF is a crucial tool with real-world applications.

Attribution:

• This article was inspired by a GitHub repository, but due to the nature of the content (mathematical concepts), specific attribution to individual contributors is not possible. However, the community of developers and mathematicians on GitHub serves as a valuable resource for learning about various mathematical concepts.