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GCF of 4 and 24

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

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

What is GCF of 4 and 24?

Answer: GCF of 4 and 24 is 4.

Explanation:

The GCF of two non-zero integers, x(4) and y(24), is the greatest positive integer m(4) that divides both x(4) and y(24) without any remainder.

Methods to Find GCF of 4 and 24

Let's look at the different methods for finding the GCF of 4 and 24.

Listing Common Factors
Long Division Method
Prime Factorization Method

GCF of 4 and 24 by Listing Common Factors

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

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

GCF of 4 and 24 by Long Division

GCF of 4 and 24 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 24 (larger number) by 4 (smaller number).
Step 2: Since the remainder = 0, the divisor (4) is the GCF of 4 and 24.

The corresponding divisor (4) is the GCF of 4 and 24.

GCF of 4 and 24 by Prime Factorization

Prime factorization of 4 and 24 is (2 × 2) and (2 × 2 × 2 × 3) respectively. As visible, 4 and 24 have common prime factors. Hence, the GCF of 4 and 24 is 2 × 2 = 4.

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GCF of 4 and 24 Examples

Example 1: Find the greatest number that divides 4 and 24 exactly.

Solution:

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

Solution:

Given: GCF (x, 24) = 4 and LCM (x, 24) = 24
∵ GCF × LCM = 24 × (x)
⇒ x = (GCF × LCM)/24
⇒ x = (4 × 24)/24
⇒ x = 4
Therefore, the other number is 4.
Example 3: The product of two numbers is 96. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and product of numbers = 96
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 96/4
Therefore, the LCM is 24.

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FAQs on GCF of 4 and 24

What is the GCF of 4 and 24?

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

How to Find the GCF of 4 and 24 by Long Division Method?

To find the GCF of 4, 24 using long division method, 24 is divided by 4. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

How to Find the GCF of 4 and 24 by Prime Factorization?

To find the GCF of 4 and 24, we will find the prime factorization of the given numbers, i.e. 4 = 2 × 2; 24 = 2 × 2 × 2 × 3.
⇒ Since 2, 2 are common terms in the prime factorization of 4 and 24. Hence, GCF(4, 24) = 2 × 2 = 4
☛ What are Prime Numbers?

What are the Methods to Find GCF of 4 and 24?

There are three commonly used methods to find the GCF of 4 and 24.

By Euclidean Algorithm
By Prime Factorization
By Long Division

If the GCF of 24 and 4 is 4, Find its LCM.

GCF(24, 4) × LCM(24, 4) = 24 × 4
Since the GCF of 24 and 4 = 4
⇒ 4 × LCM(24, 4) = 96
Therefore, LCM = 24
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What is the Relation Between LCM and GCF of 4, 24?

The following equation can be used to express the relation between Least Common Multiple and GCF of 4 and 24, i.e. GCF × LCM = 4 × 24.

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