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 56 and 35 = 7
- GCF of 40 and 100 = 20
- GCF of 45 and 120 = 15
- GCF of 52 and 78 = 26
- GCF of 12 and 45 = 3
- GCF of 22 and 33 = 11
- GCF of 64 and 120 = 8
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.
