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GCF of 24 and 48

GCF of 24 and 48 is the largest possible number that divides 24 and 48 exactly without any remainder. The factors of 24 and 48 are 1, 2, 3, 4, 6, 8, 12, 24 and 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 respectively. There are 3 commonly used methods to find the GCF of 24 and 48 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 24 and 48
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 24 and 48?

Answer: GCF of 24 and 48 is 24.

Explanation:

The GCF of two non-zero integers, x(24) and y(48), is the greatest positive integer m(24) that divides both x(24) and y(48) without any remainder.

Methods to Find GCF of 24 and 48

The methods to find the GCF of 24 and 48 are explained below.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 24 and 48 by Prime Factorization

Prime factorization of 24 and 48 is (2 × 2 × 2 × 3) and (2 × 2 × 2 × 2 × 3) respectively. As visible, 24 and 48 have common prime factors. Hence, the GCF of 24 and 48 is 2 × 2 × 2 × 3 = 24.

GCF of 24 and 48 by Listing Common Factors

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

There are 8 common factors of 24 and 48, that are 1, 2, 3, 4, 6, 8, 12, and 24. Therefore, the greatest common factor of 24 and 48 is 24.

GCF of 24 and 48 by Long Division

GCF of 24 and 48 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 48 (larger number) by 24 (smaller number).
Step 2: Since the remainder = 0, the divisor (24) is the GCF of 24 and 48.

The corresponding divisor (24) is the GCF of 24 and 48.

☛ Also Check:

GCF of 24 and 48 Examples

Example 1: The product of two numbers is 1152. If their GCF is 24, what is their LCM?

Solution:

Given: GCF = 24 and product of numbers = 1152
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1152/24
Therefore, the LCM is 48.
Example 2: Find the greatest number that divides 24 and 48 exactly.

Solution:

The greatest number that divides 24 and 48 exactly is their greatest common factor, i.e. GCF of 24 and 48.
⇒ Factors of 24 and 48:
- Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Therefore, the GCF of 24 and 48 is 24.
Example 3: Find the GCF of 24 and 48, if their LCM is 48.

Solution:

∵ LCM × GCF = 24 × 48
⇒ GCF(24, 48) = (24 × 48)/48 = 24
Therefore, the greatest common factor of 24 and 48 is 24.

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FAQs on GCF of 24 and 48

What is the GCF of 24 and 48?

The GCF of 24 and 48 is 24. To calculate the greatest common factor (GCF) of 24 and 48, we need to factor each number (factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24; factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48) and choose the greatest factor that exactly divides both 24 and 48, i.e., 24.

What are the Methods to Find GCF of 24 and 48?

There are three commonly used methods to find the GCF of 24 and 48.

By Prime Factorization
By Long Division
By Euclidean Algorithm

How to Find the GCF of 24 and 48 by Long Division Method?

To find the GCF of 24, 48 using long division method, 48 is divided by 24. The corresponding divisor (24) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 24, 48?

The following equation can be used to express the relation between LCM and GCF of 24 and 48, i.e. GCF × LCM = 24 × 48.

How to Find the GCF of 24 and 48 by Prime Factorization?

To find the GCF of 24 and 48, we will find the prime factorization of the given numbers, i.e. 24 = 2 × 2 × 2 × 3; 48 = 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 2, 2, 3 are common terms in the prime factorization of 24 and 48. Hence, GCF(24, 48) = 2 × 2 × 2 × 3 = 24
☛ Prime Numbers

If the GCF of 48 and 24 is 24, Find its LCM.

GCF(48, 24) × LCM(48, 24) = 48 × 24
Since the GCF of 48 and 24 = 24
⇒ 24 × LCM(48, 24) = 1152
Therefore, LCM = 48
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