what is the gcf of 48 and 80

Guri Bee

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20-10-2024

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Finding the Greatest Common Factor (GCF) of 48 and 80

The greatest common factor (GCF) of two numbers is the largest number that divides both of them evenly. Let's explore how to find the GCF of 48 and 80.

Methods for Finding the GCF

There are a few different methods to find the GCF:

1. Listing Factors:

• List the factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
• List the factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

The greatest common factor is the largest number that appears in both lists: 16.

2. Prime Factorization:

• Prime factorization of 48: 2 x 2 x 2 x 2 x 3
• Prime factorization of 80: 2 x 2 x 2 x 2 x 5

Identify the common prime factors and their lowest powers: 2 x 2 x 2 x 2 = 16. Therefore, the GCF of 48 and 80 is 16.

3. Euclidean Algorithm:

The Euclidean algorithm is a more efficient method for finding the GCF, especially for larger numbers. It involves repeated division:

1. Divide the larger number by the smaller number: 80 ÷ 48 = 1 remainder 32.
2. Replace the larger number with the smaller number, and the smaller number with the remainder: 48 ÷ 32 = 1 remainder 16.
3. Continue dividing until the remainder is 0. The last non-zero remainder is the GCF: 32 ÷ 16 = 2 remainder 0.

Therefore, the GCF of 48 and 80 is 16.

Applications of GCF

Finding the GCF has practical applications in various fields, including:

• Simplifying fractions: The GCF can be used to simplify a fraction by dividing both the numerator and denominator by the GCF.
• Dividing objects into equal groups: The GCF helps determine the largest possible group size when dividing objects into equal groups.
• Solving problems involving common factors: GCF can be used to find the common factors between two or more numbers, which is useful in various mathematical problems.

Conclusion

The GCF of 48 and 80 is 16. This can be found using various methods, including listing factors, prime factorization, and the Euclidean algorithm. Understanding the GCF is essential for solving various mathematical problems and simplifying fractions.