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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 non-zero 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 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.

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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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