GCF of 2 and 8 is the largest possible number that divides 2 and 8 exactly without any remainder. The factors of 2 and 8 are 1, 2 and 1, 2, 4, 8 respectively. There are 3 commonly used methods to find the GCF of 2 and 8 - long division, Euclidean algorithm, and prime factorization.
| 1. | GCF of 2 and 8 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 2 and 8?
Answer: GCF of 2 and 8 is 2.
Explanation:
The GCF of two non-zero integers, x(2) and y(8), is the greatest positive integer m(2) that divides both x(2) and y(8) without any remainder.
Methods to Find GCF of 2 and 8
The methods to find the GCF of 2 and 8 are explained below.
- Using Euclid's Algorithm
- Long Division Method
- Listing Common Factors
GCF of 2 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 = 2
- GCF(8, 2) = GCF(2, 8 mod 2) = GCF(2, 0)
- GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 2 and 8 is 2.
GCF of 2 and 8 by Long Division
GCF of 2 and 8 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 8 (larger number) by 2 (smaller number).
- Step 2: Since the remainder = 0, the divisor (2) is the GCF of 2 and 8.
The corresponding divisor (2) is the GCF of 2 and 8.
GCF of 2 and 8 by Listing Common Factors
- Factors of 2: 1, 2
- Factors of 8: 1, 2, 4, 8
There are 2 common factors of 2 and 8, that are 1 and 2. Therefore, the greatest common factor of 2 and 8 is 2.
☛ Also Check:
- GCF of 4 and 16 = 4
- GCF of 5 and 8 = 1
- GCF of 33 and 66 = 33
- GCF of 72 and 90 = 18
- GCF of 60 and 90 = 30
- GCF of 18 and 60 = 6
- GCF of 14 and 49 = 7
GCF of 2 and 8 Examples
Example 1: For two numbers, GCF = 2 and LCM = 8. If one number is 8, find the other number.
Solution:
Given: GCF (y, 8) = 2 and LCM (y, 8) = 8
∵ GCF × LCM = 8 × (y)
⇒ y = (GCF × LCM)/8
⇒ y = (2 × 8)/8
⇒ y = 2
Therefore, the other number is 2.Example 2: Find the greatest number that divides 2 and 8 exactly.
Solution:
The greatest number that divides 2 and 8 exactly is their greatest common factor, i.e. GCF of 2 and 8.
⇒ Factors of 2 and 8:- Factors of 2 = 1, 2
- Factors of 8 = 1, 2, 4, 8
Therefore, the GCF of 2 and 8 is 2.
Example 3: Find the GCF of 2 and 8, if their LCM is 8.
Solution:
∵ LCM × GCF = 2 × 8
⇒ GCF(2, 8) = (2 × 8)/8 = 2
Therefore, the greatest common factor of 2 and 8 is 2.
Show Solution >
go to slidego to slidego to slide
Ready to see the world through math’s eyes?
Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.
Book a Free Trial Class
FAQs on GCF of 2 and 8
What is the GCF of 2 and 8?
The GCF of 2 and 8 is 2. To calculate the greatest common factor (GCF) of 2 and 8, we need to factor each number (factors of 2 = 1, 2; factors of 8 = 1, 2, 4, 8) and choose the greatest factor that exactly divides both 2 and 8, i.e., 2.
What are the Methods to Find GCF of 2 and 8?
There are three commonly used methods to find the GCF of 2 and 8.
- By Long Division
- By Listing Common Factors
- By Prime Factorization
How to Find the GCF of 2 and 8 by Prime Factorization?
To find the GCF of 2 and 8, we will find the prime factorization of the given numbers, i.e. 2 = 2; 8 = 2 × 2 × 2.
⇒ Since 2 is the only common prime factor of 2 and 8. Hence, GCF (2, 8) = 2.
☛ What are Prime Numbers?
What is the Relation Between LCM and GCF of 2, 8?
The following equation can be used to express the relation between LCM and GCF of 2 and 8, i.e. GCF × LCM = 2 × 8.
If the GCF of 8 and 2 is 2, Find its LCM.
GCF(8, 2) × LCM(8, 2) = 8 × 2
Since the GCF of 8 and 2 = 2
⇒ 2 × LCM(8, 2) = 16
Therefore, LCM = 8
☛ Greatest Common Factor Calculator
How to Find the GCF of 2 and 8 by Long Division Method?
To find the GCF of 2, 8 using long division method, 8 is divided by 2. The corresponding divisor (2) when remainder equals 0 is taken as GCF.
