# GCF of 8 and 20

Created by: Team Maths - Examples.com, Last Updated: August 19, 2024

## GCF of 8 and 20

The greatest common factor (GCF) of 8 and 20 is 4. This result can be derived using several methods, including prime factorization, listing common factors, or applying the Euclidean algorithm. In prime factorization, 8 is expressed as 2³ and 20 as 2²×5 The common factor here is 2, and the lowest power is 2², leading to a GCF of 4. Listing the factors of 8 (1, 2, 4, 8) and 20 (1, 2, 4, 5, 10, 20) also shows that the highest shared factor is 4. The Euclidean algorithm, using successive division, will confirm that 4 is indeed the largest number that divides both 8 and 20 without a remainder, thus demonstrating its role as the GCF of these numbers.

## GCF of 8 and 20 by Prime Factorization Method.

To find the greatest common factor (GCF) of 8 and 20 using the prime factorization method, follow these steps:

Step 1: Prime factorize both numbers:

For 8: 8 = 2³

For 20: 20 = 2² × 5

Step 2: Identify the common prime factors and their lowest powers:

The common prime factor between 8 and 20 is 2. The lowest power of 2 that appears in both factorizations is 2².

Step 3: Multiply the common prime factors with their lowest powers to determine the GCF:

GCF = 2² = 4

Therefore, the greatest common factor (GCF) of 8 and 20 by the prime factorization method is 4.

## GCF of 8 and 20 by Long Division Method.

To find the greatest common factor (GCF) of 8 and 20 using the long division method:

Step 1: Start by dividing the larger number (20) by the smaller number (8).

20 ÷ 8 = 2  with a remainder of 4.

Step 2: Then, take the divisor (8) and divide it by the remainder (4).

8 ÷ 4 = 2 with a remainder of 0.

Since the remainder is now 0, the division process stops here.

Step 3: The divisors at this step where the remainder becomes zero is the greatest common factor (GCF).

GCF = 4.

Therefore, the greatest common factor (GCF) of 8 and 20 by the long division method is 4.

## GCF of 8 and 20 by Listing Common Factors.

To find the greatest common factor (GCF) of 8 and 20 by listing common factors:

Step 1: List the factors of each number.

Factors of 8: 1, 2, 4, 8

Factors of 20: 1, 2, 4, 5, 10, 20

Step 2: Identify the common factors.

Common factors: 1, 2, 4

Step 3: Determine the greatest common factor.

GCF = 4.

Therefore, the greatest common factor (GCF) of 8 and 20 by listing common factors is 4.

## Is there a way to visually represent the GCF of 8 and 20?

Is there a way to visually represent the GCF of 8 and 20?

## What problems can be solved by knowing the GCF of 8 and 20?

Problems involving dividing or sharing quantities in ratios, simplifying algebraic fractions, and more.

## Why is understanding the GCF important in mathematics?

It aids in simplifying expressions and solving problems involving ratios and proportions.

## What is the fastest method to find the GCF of 8 and 20?

Listing common factors might be the quickest for small numbers like these.

## What other methods are there to find the GCF of 8 and 20 besides prime factorization?

Long division and listing common factors are also effective methods.

## How do you calculate the GCF of 8 and 20?

You can calculate the GCF using methods like prime factorization, listing common factors, or long division.

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