GCF of 4 and 8 is the largest possible number that divides 4 and 8 exactly without any remainder. The factors of 4 and 8 are 1, 2, 4 and 1, 2, 4, 8 respectively. There are 3 commonly used methods to find the GCF of 4 and 8 - prime factorization, long division, and Euclidean algorithm.
| 1. | GCF of 4 and 8 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 4 and 8?
Answer: GCF of 4 and 8 is 4.
Explanation:
The GCF of two non-zero integers, x(4) and y(8), is the greatest positive integer m(4) that divides both x(4) and y(8) without any remainder.
Methods to Find GCF of 4 and 8
Let's look at the different methods for finding the GCF of 4 and 8.
- Prime Factorization Method
- Using Euclid's Algorithm
- Listing Common Factors
GCF of 4 and 8 by Prime Factorization
Prime factorization of 4 and 8 is (2 × 2) and (2 × 2 × 2) respectively. As visible, 4 and 8 have common prime factors. Hence, the GCF of 4 and 8 is 2 × 2 = 4.
GCF of 4 and 8 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 = 8 and Y = 4
- GCF(8, 4) = GCF(4, 8 mod 4) = GCF(4, 0)
- GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 4 and 8 is 4.
GCF of 4 and 8 by Listing Common Factors
- Factors of 4: 1, 2, 4
- Factors of 8: 1, 2, 4, 8
There are 3 common factors of 4 and 8, that are 1, 2, and 4. Therefore, the greatest common factor of 4 and 8 is 4.
☛ Also Check:
- GCF of 21 and 30 = 3
- GCF of 6 and 18 = 6
- GCF of 10 and 30 = 10
- GCF of 3 and 15 = 3
- GCF of 24 and 84 = 12
- GCF of 20 and 36 = 4
- GCF of 8 and 24 = 8
GCF of 4 and 8 Examples
Example 1: Find the GCF of 4 and 8, if their LCM is 8.
Solution:
∵ LCM × GCF = 4 × 8
⇒ GCF(4, 8) = (4 × 8)/8 = 4
Therefore, the greatest common factor of 4 and 8 is 4.Example 2: Find the greatest number that divides 4 and 8 exactly.
Solution:
The greatest number that divides 4 and 8 exactly is their greatest common factor, i.e. GCF of 4 and 8.
⇒ Factors of 4 and 8:- Factors of 4 = 1, 2, 4
- Factors of 8 = 1, 2, 4, 8
Therefore, the GCF of 4 and 8 is 4.
Example 3: For two numbers, GCF = 4 and LCM = 8. If one number is 4, find the other number.
Solution:
Given: GCF (y, 4) = 4 and LCM (y, 4) = 8
∵ GCF × LCM = 4 × (y)
⇒ y = (GCF × LCM)/4
⇒ y = (4 × 8)/4
⇒ y = 8
Therefore, the other number is 8.
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FAQs on GCF of 4 and 8
What is the GCF of 4 and 8?
The GCF of 4 and 8 is 4. To calculate the greatest common factor of 4 and 8, we need to factor each number (factors of 4 = 1, 2, 4; factors of 8 = 1, 2, 4, 8) and choose the greatest factor that exactly divides both 4 and 8, i.e., 4.
How to Find the GCF of 4 and 8 by Long Division Method?
To find the GCF of 4, 8 using long division method, 8 is divided by 4. The corresponding divisor (4) when remainder equals 0 is taken as GCF.
If the GCF of 8 and 4 is 4, Find its LCM.
GCF(8, 4) × LCM(8, 4) = 8 × 4
Since the GCF of 8 and 4 = 4
⇒ 4 × LCM(8, 4) = 32
Therefore, LCM = 8
☛ Greatest Common Factor Calculator
What are the Methods to Find GCF of 4 and 8?
There are three commonly used methods to find the GCF of 4 and 8.
- By Prime Factorization
- By Long Division
- By Euclidean Algorithm
What is the Relation Between LCM and GCF of 4, 8?
The following equation can be used to express the relation between Least Common Multiple and GCF of 4 and 8, i.e. GCF × LCM = 4 × 8.
How to Find the GCF of 4 and 8 by Prime Factorization?
To find the GCF of 4 and 8, we will find the prime factorization of the given numbers, i.e. 4 = 2 × 2; 8 = 2 × 2 × 2.
⇒ Since 2, 2 are common terms in the prime factorization of 4 and 8. Hence, GCF(4, 8) = 2 × 2 = 4
☛ What is a Prime Number?
