GCF of 2 and 3 is the largest possible number that divides 2 and 3 exactly without any remainder. The factors of 2 and 3 are 1, 2 and 1, 3 respectively. There are 3 commonly used methods to find the GCF of 2 and 3 - long division, prime factorization, and Euclidean algorithm.
| 1. | GCF of 2 and 3 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 2 and 3?
Answer: GCF of 2 and 3 is 1.
Explanation:
The GCF of two non-zero integers, x(2) and y(3), is the greatest positive integer m(1) that divides both x(2) and y(3) without any remainder.
Methods to Find GCF of 2 and 3
The methods to find the GCF of 2 and 3 are explained below.
- Listing Common Factors
- Long Division Method
- Using Euclid's Algorithm
GCF of 2 and 3 by Listing Common Factors
- Factors of 2: 1, 2
- Factors of 3: 1, 3
Since, 1 is the only common factor between 2 and 3. The Greatest Common Factor of 2 and 3 is 1.
GCF of 2 and 3 by Long Division
GCF of 2 and 3 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 3 (larger number) by 2 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (2) by the remainder (1).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (1) is the GCF of 2 and 3.
GCF of 2 and 3 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 = 3 and Y = 2
- GCF(3, 2) = GCF(2, 3 mod 2) = GCF(2, 1)
- GCF(2, 1) = GCF(1, 2 mod 1) = GCF(1, 0)
- GCF(1, 0) = 1 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 2 and 3 is 1.
☛ Also Check:
- GCF of 18 and 21 = 3
- GCF of 24 and 64 = 8
- GCF of 14 and 35 = 7
- GCF of 18 and 28 = 2
- GCF of 25 and 100 = 25
- GCF of 45 and 90 = 45
- GCF of 15 and 50 = 5
GCF of 2 and 3 Examples
Example 1: Find the greatest number that divides 2 and 3 exactly.
Solution:
The greatest number that divides 2 and 3 exactly is their greatest common factor, i.e. GCF of 2 and 3.
⇒ Factors of 2 and 3:- Factors of 2 = 1, 2
- Factors of 3 = 1, 3
Therefore, the GCF of 2 and 3 is 1.
Example 2: For two numbers, GCF = 1 and LCM = 6. If one number is 2, find the other number.
Solution:
Given: GCF (x, 2) = 1 and LCM (x, 2) = 6
∵ GCF × LCM = 2 × (x)
⇒ x = (GCF × LCM)/2
⇒ x = (1 × 6)/2
⇒ x = 3
Therefore, the other number is 3.Example 3: Find the GCF of 2 and 3, if their LCM is 6.
Solution:
∵ LCM × GCF = 2 × 3
⇒ GCF(2, 3) = (2 × 3)/6 = 1
Therefore, the greatest common factor of 2 and 3 is 1.
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FAQs on GCF of 2 and 3
What is the GCF of 2 and 3?
The GCF of 2 and 3 is 1. To calculate the GCF (Greatest Common Factor) of 2 and 3, we need to factor each number (factors of 2 = 1, 2; factors of 3 = 1, 3) and choose the greatest factor that exactly divides both 2 and 3, i.e., 1.
What is the Relation Between LCM and GCF of 2, 3?
The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 2 and 3, i.e. GCF × LCM = 2 × 3.
What are the Methods to Find GCF of 2 and 3?
There are three commonly used methods to find the GCF of 2 and 3.
- By Long Division
- By Euclidean Algorithm
- By Prime Factorization
If the GCF of 3 and 2 is 1, Find its LCM.
GCF(3, 2) × LCM(3, 2) = 3 × 2
Since the GCF of 3 and 2 = 1
⇒ 1 × LCM(3, 2) = 6
Therefore, LCM = 6
☛ GCF Calculator
How to Find the GCF of 2 and 3 by Prime Factorization?
To find the GCF of 2 and 3, we will find the prime factorization of the given numbers, i.e. 2 = 2; 3 = 3.
⇒ There is no common prime factor for 2 and 3. Hence, GCF (2, 3) = 1.
☛ Prime Number
How to Find the GCF of 2 and 3 by Long Division Method?
To find the GCF of 2, 3 using long division method, 3 is divided by 2. The corresponding divisor (1) when remainder equals 0 is taken as GCF.
