# GCF of 24 and 30

Created by: Team Maths - Examples.com, Last Updated: May 31, 2024

## GCF of 24 and 30

The greatest common factor (GCF) of 24 and 30 is 6. This can be efficiently determined using several straightforward methods such as listing factors, prime factorization, or the Euclidean algorithm. When listing factors, you find that the common factors of 24 (1, 2, 3, 4, 6, 8, 12, 24) and 30 (1, 2, 3, 5, 6, 10, 15, 30) are 1, 2, 3, and 6, with 6 being the largest. Prime factorization reveals that 24 is 2³ × 3 and 30 is 2 × 3 × 5, with the common prime factors being 2 and 3, which multiply to 6. The Euclidean algorithm, using division and remainders, also identifies 6 as the GCF. This value is key for simplifying fractions and other calculations involving these numbers.

## GCF of 24 and 30 by Prime Factorization Method.

To find the greatest common factor (GCF) of 24 and 30 using the prime factorization method:

Step 1: Prime factorize both numbers:

For 24: 24 = 2³ × 3

For 30: 30 = 2 × 3 × 5

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

• The common prime factors between 24 and 30 are 2 and 3. The lowest power of 2 present in both factorizations is 2¹, and the lowest power of 3 is 3¹.

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

GCF = 2¹ × 3¹ = 2 × 3 = 6

Therefore, the greatest common factor (GCF) of 24 and 30 by the prime factorization method is 6.

## GCF of 24 and 30 by Long Division Method.

To find the greatest common factor (GCF) of 24 and 30 using the long division method:

Step 1: Start by dividing the larger number (30) by the smaller number (24).

30 ÷ 24 = 1 with a remainder of 6.

Step 2: Now take the remainder (6) and divide the previous divisor (24) by it.

24 ÷ 6 = 4 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 = 6.

Therefore, the greatest common factor (GCF) of 24 and 30 by the long division method is 6.

## GCF of 24 and 30 by Listing Common Factors.

To find the greatest common factor (GCF) of 24 and 30 by listing common factors:

Step 1: List the factors of each number.

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

Step 2: Identify the common factors.

• The common factors that 24 and 30 share are: 1, 2, 3, 6

Step 3: Determine the greatest common factor.

• The largest number among the common factors is 6.

Therefore, the greatest common factor (GCF) of 24 and 30 by listing common factors is 6.

## What are the factors of 24 and 30?

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24; factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.

## What is the simplest method to find the GCF of 24 and 30?

Listing factors is straightforward and effective for smaller numbers.

## Can a calculator be used to find the GCF of 24 and 30?

Yes, most scientific calculators and mathematical software can compute the GCF.

## What common mistakes do students make when finding the GCF of 24 and 30?

Confusing GCF with LCM or failing to identify all common factors.

## How does understanding the GCF of 24 and 30 help in algebra?

It is crucial for simplifying algebraic expressions and solving equations.

## What are some engaging ways to teach the GCF of 24 and 30?

Using visual aids like Venn diagrams, factor trees, and interactive quizzes.

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