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GCF of 6 and 10
GCF of 6 and 10 is the largest possible number that divides 6 and 10 exactly without any remainder. The factors of 6 and 10 are 1, 2, 3, 6 and 1, 2, 5, 10 respectively. There are 3 commonly used methods to find the GCF of 6 and 10  prime factorization, Euclidean algorithm, and long division.
1.  GCF of 6 and 10 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 6 and 10?
Answer: GCF of 6 and 10 is 2.
Explanation:
The GCF of two nonzero integers, x(6) and y(10), is the greatest positive integer m(2) that divides both x(6) and y(10) without any remainder.
Methods to Find GCF of 6 and 10
The methods to find the GCF of 6 and 10 are explained below.
 Prime Factorization Method
 Listing Common Factors
 Using Euclid's Algorithm
GCF of 6 and 10 by Prime Factorization
Prime factorization of 6 and 10 is (2 × 3) and (2 × 5) respectively. As visible, 6 and 10 have only one common prime factor i.e. 2. Hence, the GCF of 6 and 10 is 2.
GCF of 6 and 10 by Listing Common Factors
 Factors of 6: 1, 2, 3, 6
 Factors of 10: 1, 2, 5, 10
There are 2 common factors of 6 and 10, that are 1 and 2. Therefore, the greatest common factor of 6 and 10 is 2.
GCF of 6 and 10 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 = 10 and Y = 6
 GCF(10, 6) = GCF(6, 10 mod 6) = GCF(6, 4)
 GCF(6, 4) = GCF(4, 6 mod 4) = GCF(4, 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 6 and 10 is 2.
☛ Also Check:
 GCF of 36 and 84 = 12
 GCF of 72 and 80 = 8
 GCF of 64 and 32 = 32
 GCF of 72 and 108 = 36
 GCF of 30 and 42 = 6
 GCF of 25 and 45 = 5
 GCF of 2 and 5 = 1
GCF of 6 and 10 Examples

Example 1: The product of two numbers is 60. If their GCF is 2, what is their LCM?
Solution:
Given: GCF = 2 and product of numbers = 60
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 60/2
Therefore, the LCM is 30. 
Example 2: Find the greatest number that divides 6 and 10 exactly.
Solution:
The greatest number that divides 6 and 10 exactly is their greatest common factor, i.e. GCF of 6 and 10.
⇒ Factors of 6 and 10: Factors of 6 = 1, 2, 3, 6
 Factors of 10 = 1, 2, 5, 10
Therefore, the GCF of 6 and 10 is 2.

Example 3: Find the GCF of 6 and 10, if their LCM is 30.
Solution:
∵ LCM × GCF = 6 × 10
⇒ GCF(6, 10) = (6 × 10)/30 = 2
Therefore, the greatest common factor of 6 and 10 is 2.
FAQs on GCF of 6 and 10
What is the GCF of 6 and 10?
The GCF of 6 and 10 is 2. To calculate the GCF of 6 and 10, we need to factor each number (factors of 6 = 1, 2, 3, 6; factors of 10 = 1, 2, 5, 10) and choose the greatest factor that exactly divides both 6 and 10, i.e., 2.
How to Find the GCF of 6 and 10 by Long Division Method?
To find the GCF of 6, 10 using long division method, 10 is divided by 6. The corresponding divisor (2) when remainder equals 0 is taken as GCF.
What are the Methods to Find GCF of 6 and 10?
There are three commonly used methods to find the GCF of 6 and 10.
 By Long Division
 By Euclidean Algorithm
 By Prime Factorization
How to Find the GCF of 6 and 10 by Prime Factorization?
To find the GCF of 6 and 10, we will find the prime factorization of the given numbers, i.e. 6 = 2 × 3; 10 = 2 × 5.
⇒ Since 2 is the only common prime factor of 6 and 10. Hence, GCF (6, 10) = 2.
☛ What are Prime Numbers?
If the GCF of 10 and 6 is 2, Find its LCM.
GCF(10, 6) × LCM(10, 6) = 10 × 6
Since the GCF of 10 and 6 = 2
⇒ 2 × LCM(10, 6) = 60
Therefore, LCM = 30
☛ Greatest Common Factor Calculator
What is the Relation Between LCM and GCF of 6, 10?
The following equation can be used to express the relation between LCM and GCF of 6 and 10, i.e. GCF × LCM = 6 × 10.
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