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GCF of 3 and 4

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

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

What is GCF of 3 and 4?

Answer: GCF of 3 and 4 is 1.

Explanation:

The GCF of two non-zero integers, x(3) and y(4), is the greatest positive integer m(1) that divides both x(3) and y(4) without any remainder.

Methods to Find GCF of 3 and 4

The methods to find the GCF of 3 and 4 are explained below.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

GCF of 3 and 4 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 = 4 and Y = 3

GCF(4, 3) = GCF(3, 4 mod 3) = GCF(3, 1)
GCF(3, 1) = GCF(1, 3 mod 1) = GCF(1, 0)
GCF(1, 0) = 1 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 3 and 4 is 1.

GCF of 3 and 4 by Long Division

GCF of 3 and 4 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 4 (larger number) by 3 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (3) by the remainder (1).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 3 and 4.

GCF of 3 and 4 by Listing Common Factors

Factors of 3: 1, 3
Factors of 4: 1, 2, 4

Since, 1 is the only common factor between 3 and 4. The Greatest Common Factor of 3 and 4 is 1.

☛ Also Check:

GCF of 3 and 4 Examples

Example 1: Find the greatest number that divides 3 and 4 exactly.

Solution:

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

Solution:

∵ LCM × GCF = 3 × 4
⇒ GCF(3, 4) = (3 × 4)/12 = 1
Therefore, the greatest common factor of 3 and 4 is 1.
Example 3: For two numbers, GCF = 1 and LCM = 12. If one number is 3, find the other number.

Solution:

Given: GCF (x, 3) = 1 and LCM (x, 3) = 12
∵ GCF × LCM = 3 × (x)
⇒ x = (GCF × LCM)/3
⇒ x = (1 × 12)/3
⇒ x = 4
Therefore, the other number is 4.

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FAQs on GCF of 3 and 4

What is the GCF of 3 and 4?

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

What are the Methods to Find GCF of 3 and 4?

There are three commonly used methods to find the GCF of 3 and 4.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the GCF of 3 and 4 by Prime Factorization?

To find the GCF of 3 and 4, we will find the prime factorization of the given numbers, i.e. 3 = 3; 4 = 2 × 2.
⇒ There is no common prime factor for 3 and 4. Hence, GCF (3, 4) = 1.
☛ What is a Prime Number?

What is the Relation Between LCM and GCF of 3, 4?

The following equation can be used to express the relation between Least Common Multiple and GCF of 3 and 4, i.e. GCF × LCM = 3 × 4.

If the GCF of 4 and 3 is 1, Find its LCM.

GCF(4, 3) × LCM(4, 3) = 4 × 3
Since the GCF of 4 and 3 = 1
⇒ 1 × LCM(4, 3) = 12
Therefore, LCM = 12
☛ GCF Calculator

How to Find the GCF of 3 and 4 by Long Division Method?

To find the GCF of 3, 4 using long division method, 4 is divided by 3. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

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