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GCF of 6 and 30

GCF of 6 and 30 is the largest possible number that divides 6 and 30 exactly without any remainder. The factors of 6 and 30 are 1, 2, 3, 6 and 1, 2, 3, 5, 6, 10, 15, 30 respectively. There are 3 commonly used methods to find the GCF of 6 and 30 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 6 and 30
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 6 and 30?

Answer: GCF of 6 and 30 is 6.

Explanation:

The GCF of two non-zero integers, x(6) and y(30), is the greatest positive integer m(6) that divides both x(6) and y(30) without any remainder.

Methods to Find GCF of 6 and 30

Let's look at the different methods for finding the GCF of 6 and 30.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 6 and 30 by Prime Factorization

Prime factorization of 6 and 30 is (2 × 3) and (2 × 3 × 5) respectively. As visible, 6 and 30 have common prime factors. Hence, the GCF of 6 and 30 is 2 × 3 = 6.

GCF of 6 and 30 by Listing Common Factors

Factors of 6: 1, 2, 3, 6
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

There are 4 common factors of 6 and 30, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 6 and 30 is 6.

GCF of 6 and 30 by Long Division

GCF of 6 and 30 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 30 (larger number) by 6 (smaller number).
Step 2: Since the remainder = 0, the divisor (6) is the GCF of 6 and 30.

The corresponding divisor (6) is the GCF of 6 and 30.

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GCF of 6 and 30 Examples

Example 1: Find the greatest number that divides 6 and 30 exactly.

Solution:

The greatest number that divides 6 and 30 exactly is their greatest common factor, i.e. GCF of 6 and 30.
⇒ Factors of 6 and 30:
- Factors of 6 = 1, 2, 3, 6
- Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
Therefore, the GCF of 6 and 30 is 6.
Example 2: The product of two numbers is 180. If their GCF is 6, what is their LCM?

Solution:

Given: GCF = 6 and product of numbers = 180
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 180/6
Therefore, the LCM is 30.
Example 3: For two numbers, GCF = 6 and LCM = 30. If one number is 6, find the other number.

Solution:

Given: GCF (y, 6) = 6 and LCM (y, 6) = 30
∵ GCF × LCM = 6 × (y)
⇒ y = (GCF × LCM)/6
⇒ y = (6 × 30)/6
⇒ y = 30
Therefore, the other number is 30.

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FAQs on GCF of 6 and 30

What is the GCF of 6 and 30?

The GCF of 6 and 30 is 6. To calculate the GCF (Greatest Common Factor) of 6 and 30, we need to factor each number (factors of 6 = 1, 2, 3, 6; factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30) and choose the greatest factor that exactly divides both 6 and 30, i.e., 6.

How to Find the GCF of 6 and 30 by Long Division Method?

To find the GCF of 6, 30 using long division method, 30 is divided by 6. The corresponding divisor (6) when remainder equals 0 is taken as GCF.

If the GCF of 30 and 6 is 6, Find its LCM.

GCF(30, 6) × LCM(30, 6) = 30 × 6
Since the GCF of 30 and 6 = 6
⇒ 6 × LCM(30, 6) = 180
Therefore, LCM = 30
☛ GCF Calculator

What is the Relation Between LCM and GCF of 6, 30?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 6 and 30, i.e. GCF × LCM = 6 × 30.

How to Find the GCF of 6 and 30 by Prime Factorization?

To find the GCF of 6 and 30, we will find the prime factorization of the given numbers, i.e. 6 = 2 × 3; 30 = 2 × 3 × 5.
⇒ Since 2, 3 are common terms in the prime factorization of 6 and 30. Hence, GCF(6, 30) = 2 × 3 = 6
☛ Prime Number

What are the Methods to Find GCF of 6 and 30?

There are three commonly used methods to find the GCF of 6 and 30.

By Prime Factorization
By Euclidean Algorithm
By Long Division

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