GCF of 24 and 40

Created by: Team Maths - Examples.com, Last Updated: May 29, 2024

GCF of 24 and 40

To find the Greatest Common Factor (GCF) of 24 and 40, list the factors of each numbers: the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24, while the factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40. The common factors are 1, 2, 4, and 8, with the greatest common factor being 8. Therefore, the GCF of 24 and 40 is 8.

Methods to Find GCF of 24 and 40

1. Prime Factorization Method
2. Long Division Method
3. Listing Common Factors

GCF of 24 and 40 by Prime Factorization Method.

To find the Greatest Common Factor (GCF) of 24 and 40 using the prime factorization method, follow these steps:

Step 1: Find the prime factorization of each number

Prime factorization of 24:

24 = 2 × 2 × 2 × 3 = 2³ × 3

Prime factorization of 40:

40 = 2 × 2 × 2 × 5 = 2³ × 5

Step 2: Identify the common prime factors

The common prime factors of 24 and 40 are 2, and both numbers have 2³ in their factorization.

Step 3: Multiply the common prime factors

The common prime factor is 2³.

GCF of 24 and 40 by Long Division Method.

To find the Greatest Common Factor (GCF) of 24 and 40 using the long division method, follow these steps:

Step 1: Divide the larger number by the smaller number

40 ÷ 24 = 1 with a remainder of 16.

Step 2: Replace the larger number with the smaller number, and the smaller number with the remainder

Now, we have 24 and 16.

Step 3: Repeat the division

24 ÷ 16 = 1 with a remainder of 8.

Step 4: Continue the process

16 ÷ 8 = 2 with a remainder of 0.

Step 5: When the remainder is 0, the divisors is the GCF

The last non-zero remainder is 8. So, the GCF of 24 and 40 is 8.

GCF of 24 and 40 by Listing Common Factors.

To find the Greatest Common Factor (GCF) of 24 and 40 by listing common factors, follow these steps:

Step 1: List the factors of each number

Factors of 24:

• 1, 2, 3, 4, 6, 8, 12, 24

Factors of 40:

• 1, 2, 4, 5, 8, 10, 20, 40

Step 2: Identify the common factors

Common factors of 24 and 40:

• 1, 2, 4, 8

Step 3: Determine the greatest common factor

The largest common factor is 8. Therefore, the GCF of 24 and 40 is 8.

What is the LCM of 24 and 40?

The least common multiple (LCM) of 24 and 40 is 120.

How is the GCF used in simplifying fractions?

Divide both the numerator and denominator by the GCF.

Why is the GCF of 24 and 40 important?

It simplifies fractions and helps solve problems involving divisibility.

What are the common factors of 24 and 40?

The common factors are 1, 2, 4, and 8.

How do you find the GCF of 24 and 40?

You can find it using long division, prime factorization, or by listing common factors.

Text prompt