GCF of 8 and 10
GCF of 8 and 10 is the largest possible number that divides 8 and 10 exactly without any remainder. The factors of 8 and 10 are 1, 2, 4, 8 and 1, 2, 5, 10 respectively. There are 3 commonly used methods to find the GCF of 8 and 10  Euclidean algorithm, long division, and prime factorization.
1.  GCF of 8 and 10 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 8 and 10?
Answer: GCF of 8 and 10 is 2.
Explanation:
The GCF of two nonzero integers, x(8) and y(10), is the greatest positive integer m(2) that divides both x(8) and y(10) without any remainder.
Methods to Find GCF of 8 and 10
Let's look at the different methods for finding the GCF of 8 and 10.
 Prime Factorization Method
 Long Division Method
 Listing Common Factors
GCF of 8 and 10 by Prime Factorization
Prime factorization of 8 and 10 is (2 × 2 × 2) and (2 × 5) respectively. As visible, 8 and 10 have only one common prime factor i.e. 2. Hence, the GCF of 8 and 10 is 2.
GCF of 8 and 10 by Long Division
GCF of 8 and 10 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 10 (larger number) by 8 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (8) by the remainder (2).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (2) is the GCF of 8 and 10.
GCF of 8 and 10 by Listing Common Factors
 Factors of 8: 1, 2, 4, 8
 Factors of 10: 1, 2, 5, 10
There are 2 common factors of 8 and 10, that are 1 and 2. Therefore, the greatest common factor of 8 and 10 is 2.
☛ Also Check:
 GCF of 8 and 6 = 2
 GCF of 6 and 24 = 6
 GCF of 63 and 54 = 9
 GCF of 5 and 35 = 5
 GCF of 36 and 84 = 12
 GCF of 6 and 21 = 3
 GCF of 15 and 75 = 15
GCF of 8 and 10 Examples

Example 1: For two numbers, GCF = 2 and LCM = 40. If one number is 10, find the other number.
Solution:
Given: GCF (y, 10) = 2 and LCM (y, 10) = 40
∵ GCF × LCM = 10 × (y)
⇒ y = (GCF × LCM)/10
⇒ y = (2 × 40)/10
⇒ y = 8
Therefore, the other number is 8. 
Example 2: Find the greatest number that divides 8 and 10 exactly.
Solution:
The greatest number that divides 8 and 10 exactly is their greatest common factor, i.e. GCF of 8 and 10.
⇒ Factors of 8 and 10: Factors of 8 = 1, 2, 4, 8
 Factors of 10 = 1, 2, 5, 10
Therefore, the GCF of 8 and 10 is 2.

Example 3: The product of two numbers is 80. If their GCF is 2, what is their LCM?
Solution:
Given: GCF = 2 and product of numbers = 80
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 80/2
Therefore, the LCM is 40.
FAQs on GCF of 8 and 10
What is the GCF of 8 and 10?
The GCF of 8 and 10 is 2. To calculate the greatest common factor (GCF) of 8 and 10, we need to factor each number (factors of 8 = 1, 2, 4, 8; factors of 10 = 1, 2, 5, 10) and choose the greatest factor that exactly divides both 8 and 10, i.e., 2.
What is the Relation Between LCM and GCF of 8, 10?
The following equation can be used to express the relation between LCM and GCF of 8 and 10, i.e. GCF × LCM = 8 × 10.
What are the Methods to Find GCF of 8 and 10?
There are three commonly used methods to find the GCF of 8 and 10.
 By Prime Factorization
 By Long Division
 By Listing Common Factors
How to Find the GCF of 8 and 10 by Prime Factorization?
To find the GCF of 8 and 10, we will find the prime factorization of the given numbers, i.e. 8 = 2 × 2 × 2; 10 = 2 × 5.
⇒ Since 2 is the only common prime factor of 8 and 10. Hence, GCF (8, 10) = 2.
☛ What are Prime Numbers?
If the GCF of 10 and 8 is 2, Find its LCM.
GCF(10, 8) × LCM(10, 8) = 10 × 8
Since the GCF of 10 and 8 = 2
⇒ 2 × LCM(10, 8) = 80
Therefore, LCM = 40
☛ GCF Calculator
How to Find the GCF of 8 and 10 by Long Division Method?
To find the GCF of 8, 10 using long division method, 10 is divided by 8. The corresponding divisor (2) when remainder equals 0 is taken as GCF.
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