GCF of 2 and 4 is the largest possible number that divides 2 and 4 exactly without any remainder. The factors of 2 and 4 are 1, 2 and 1, 2, 4 respectively. There are 3 commonly used methods to find the GCF of 2 and 4 - long division, prime factorization, and Euclidean algorithm.
| 1. | GCF of 2 and 4 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 2 and 4?
Answer: GCF of 2 and 4 is 2.
Explanation:
The GCF of two non-zero integers, x(2) and y(4), is the greatest positive integer m(2) that divides both x(2) and y(4) without any remainder.
Methods to Find GCF of 2 and 4
Let's look at the different methods for finding the GCF of 2 and 4.
- Using Euclid's Algorithm
- Listing Common Factors
- Long Division Method
GCF of 2 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 = 2
- GCF(4, 2) = GCF(2, 4 mod 2) = GCF(2, 0)
- GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 2 and 4 is 2.
GCF of 2 and 4 by Listing Common Factors
- Factors of 2: 1, 2
- Factors of 4: 1, 2, 4
There are 2 common factors of 2 and 4, that are 1 and 2. Therefore, the greatest common factor of 2 and 4 is 2.
GCF of 2 and 4 by Long Division
GCF of 2 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 2 (smaller number).
- Step 2: Since the remainder = 0, the divisor (2) is the GCF of 2 and 4.
The corresponding divisor (2) is the GCF of 2 and 4.
☛ Also Check:
- GCF of 38 and 57 = 19
- GCF of 18 and 24 = 6
- GCF of 13 and 26 = 13
- GCF of 15 and 30 = 15
- GCF of 12 and 42 = 6
- GCF of 32 and 45 = 1
- GCF of 20 and 45 = 5
GCF of 2 and 4 Examples
Example 1: The product of two numbers is 8. If their GCF is 2, what is their LCM?
Solution:
Given: GCF = 2 and product of numbers = 8
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 8/2
Therefore, the LCM is 4.Example 2: Find the greatest number that divides 2 and 4 exactly.
Solution:
The greatest number that divides 2 and 4 exactly is their greatest common factor, i.e. GCF of 2 and 4.
⇒ Factors of 2 and 4:- Factors of 2 = 1, 2
- Factors of 4 = 1, 2, 4
Therefore, the GCF of 2 and 4 is 2.
Example 3: Find the GCF of 2 and 4, if their LCM is 4.
Solution:
∵ LCM × GCF = 2 × 4
⇒ GCF(2, 4) = (2 × 4)/4 = 2
Therefore, the greatest common factor of 2 and 4 is 2.
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FAQs on GCF of 2 and 4
What is the GCF of 2 and 4?
The GCF of 2 and 4 is 2. To calculate the greatest common factor (GCF) of 2 and 4, we need to factor each number (factors of 2 = 1, 2; factors of 4 = 1, 2, 4) and choose the greatest factor that exactly divides both 2 and 4, i.e., 2.
How to Find the GCF of 2 and 4 by Prime Factorization?
To find the GCF of 2 and 4, we will find the prime factorization of the given numbers, i.e. 2 = 2; 4 = 2 × 2.
⇒ Since 2 is the only common prime factor of 2 and 4. Hence, GCF (2, 4) = 2.
☛ Prime Numbers
What is the Relation Between LCM and GCF of 2, 4?
The following equation can be used to express the relation between Least Common Multiple and GCF of 2 and 4, i.e. GCF × LCM = 2 × 4.
How to Find the GCF of 2 and 4 by Long Division Method?
To find the GCF of 2, 4 using long division method, 4 is divided by 2. The corresponding divisor (2) when remainder equals 0 is taken as GCF.
What are the Methods to Find GCF of 2 and 4?
There are three commonly used methods to find the GCF of 2 and 4.
- By Long Division
- By Euclidean Algorithm
- By Prime Factorization
If the GCF of 4 and 2 is 2, Find its LCM.
GCF(4, 2) × LCM(4, 2) = 4 × 2
Since the GCF of 4 and 2 = 2
⇒ 2 × LCM(4, 2) = 8
Therefore, LCM = 4
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