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GCF of 3 and 24

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

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

What is GCF of 3 and 24?

Answer: GCF of 3 and 24 is 3.

Explanation:

The GCF of two non-zero integers, x(3) and y(24), is the greatest positive integer m(3) that divides both x(3) and y(24) without any remainder.

Methods to Find GCF of 3 and 24

Let's look at the different methods for finding the GCF of 3 and 24.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 3 and 24 by Long Division

GCF of 3 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 3 (smaller number).
Step 2: Since the remainder = 0, the divisor (3) is the GCF of 3 and 24.

The corresponding divisor (3) is the GCF of 3 and 24.

GCF of 3 and 24 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 24 and Y = 3

GCF(24, 3) = GCF(3, 24 mod 3) = GCF(3, 0)
GCF(3, 0) = 3 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 3 and 24 is 3.

GCF of 3 and 24 by Listing Common Factors

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

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

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GCF of 3 and 24 Examples

Example 1: The product of two numbers is 72. If their GCF is 3, what is their LCM?

Solution:

Given: GCF = 3 and product of numbers = 72
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 72/3
Therefore, the LCM is 24.
Example 2: For two numbers, GCF = 3 and LCM = 24. If one number is 24, find the other number.

Solution:

Given: GCF (z, 24) = 3 and LCM (z, 24) = 24
∵ GCF × LCM = 24 × (z)
⇒ z = (GCF × LCM)/24
⇒ z = (3 × 24)/24
⇒ z = 3
Therefore, the other number is 3.
Example 3: Find the greatest number that divides 3 and 24 exactly.

Solution:

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

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FAQs on GCF of 3 and 24

What is the GCF of 3 and 24?

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

What are the Methods to Find GCF of 3 and 24?

There are three commonly used methods to find the GCF of 3 and 24.

By Long Division
By Prime Factorization
By Listing Common Factors

If the GCF of 24 and 3 is 3, Find its LCM.

GCF(24, 3) × LCM(24, 3) = 24 × 3
Since the GCF of 24 and 3 = 3
⇒ 3 × LCM(24, 3) = 72
Therefore, LCM = 24
☛ GCF Calculator

How to Find the GCF of 3 and 24 by Prime Factorization?

To find the GCF of 3 and 24, we will find the prime factorization of the given numbers, i.e. 3 = 3; 24 = 2 × 2 × 2 × 3.
⇒ Since 3 is the only common prime factor of 3 and 24. Hence, GCF (3, 24) = 3.
☛ What is a Prime Number?

How to Find the GCF of 3 and 24 by Long Division Method?

To find the GCF of 3, 24 using long division method, 24 is divided by 3. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 3, 24?

The following equation can be used to express the relation between Least Common Multiple and GCF of 3 and 24, i.e. GCF × LCM = 3 × 24.

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