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GCF of 24 and 96

GCF of 24 and 96 is the largest possible number that divides 24 and 96 exactly without any remainder. The factors of 24 and 96 are 1, 2, 3, 4, 6, 8, 12, 24 and 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 respectively. There are 3 commonly used methods to find the GCF of 24 and 96 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 24 and 96
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 24 and 96?

Answer: GCF of 24 and 96 is 24.

Explanation:

The GCF of two non-zero integers, x(24) and y(96), is the greatest positive integer m(24) that divides both x(24) and y(96) without any remainder.

Methods to Find GCF of 24 and 96

The methods to find the GCF of 24 and 96 are explained below.

Prime Factorization Method
Long Division Method
Listing Common Factors

GCF of 24 and 96 by Prime Factorization

Prime factorization of 24 and 96 is (2 × 2 × 2 × 3) and (2 × 2 × 2 × 2 × 2 × 3) respectively. As visible, 24 and 96 have common prime factors. Hence, the GCF of 24 and 96 is 2 × 2 × 2 × 3 = 24.

GCF of 24 and 96 by Long Division

GCF of 24 and 96 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 96 (larger number) by 24 (smaller number).
Step 2: Since the remainder = 0, the divisor (24) is the GCF of 24 and 96.

The corresponding divisor (24) is the GCF of 24 and 96.

GCF of 24 and 96 by Listing Common Factors

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

There are 8 common factors of 24 and 96, that are 1, 2, 3, 4, 6, 8, 12, and 24. Therefore, the greatest common factor of 24 and 96 is 24.

☛ Also Check:

GCF of 24 and 96 Examples

Example 1: The product of two numbers is 2304. If their GCF is 24, what is their LCM?

Solution:

Given: GCF = 24 and product of numbers = 2304
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2304/24
Therefore, the LCM is 96.
Example 2: Find the greatest number that divides 24 and 96 exactly.

Solution:

The greatest number that divides 24 and 96 exactly is their greatest common factor, i.e. GCF of 24 and 96.
⇒ Factors of 24 and 96:
- Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Therefore, the GCF of 24 and 96 is 24.
Example 3: For two numbers, GCF = 24 and LCM = 96. If one number is 96, find the other number.

Solution:

Given: GCF (y, 96) = 24 and LCM (y, 96) = 96
∵ GCF × LCM = 96 × (y)
⇒ y = (GCF × LCM)/96
⇒ y = (24 × 96)/96
⇒ y = 24
Therefore, the other number is 24.

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FAQs on GCF of 24 and 96

What is the GCF of 24 and 96?

The GCF of 24 and 96 is 24. To calculate the GCF of 24 and 96, we need to factor each number (factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24; factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96) and choose the greatest factor that exactly divides both 24 and 96, i.e., 24.

How to Find the GCF of 24 and 96 by Prime Factorization?

To find the GCF of 24 and 96, we will find the prime factorization of the given numbers, i.e. 24 = 2 × 2 × 2 × 3; 96 = 2 × 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 2, 2, 3 are common terms in the prime factorization of 24 and 96. Hence, GCF(24, 96) = 2 × 2 × 2 × 3 = 24
☛ Prime Number

What are the Methods to Find GCF of 24 and 96?

There are three commonly used methods to find the GCF of 24 and 96.

By Listing Common Factors
By Long Division
By Prime Factorization

If the GCF of 96 and 24 is 24, Find its LCM.

GCF(96, 24) × LCM(96, 24) = 96 × 24
Since the GCF of 96 and 24 = 24
⇒ 24 × LCM(96, 24) = 2304
Therefore, LCM = 96
☛ Greatest Common Factor Calculator

How to Find the GCF of 24 and 96 by Long Division Method?

To find the GCF of 24, 96 using long division method, 96 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, 96?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 24 and 96, i.e. GCF × LCM = 24 × 96.

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