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GCF of 6 and 20

GCF of 6 and 20 is the largest possible number that divides 6 and 20 exactly without any remainder. The factors of 6 and 20 are 1, 2, 3, 6 and 1, 2, 4, 5, 10, 20 respectively. There are 3 commonly used methods to find the GCF of 6 and 20 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 6 and 20
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 6 and 20?

Answer: GCF of 6 and 20 is 2.

Explanation:

The GCF of two non-zero integers, x(6) and y(20), is the greatest positive integer m(2) that divides both x(6) and y(20) without any remainder.

Methods to Find GCF of 6 and 20

Let's look at the different methods for finding the GCF of 6 and 20.

Using Euclid's Algorithm
Long Division Method
Prime Factorization Method

GCF of 6 and 20 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 = 20 and Y = 6

GCF(20, 6) = GCF(6, 20 mod 6) = GCF(6, 2)
GCF(6, 2) = GCF(2, 6 mod 2) = GCF(2, 0)
GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 6 and 20 is 2.

GCF of 6 and 20 by Long Division

GCF of 6 and 20 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 20 (larger number) by 6 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (6) by the remainder (2).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 6 and 20.

GCF of 6 and 20 by Prime Factorization

Prime factorization of 6 and 20 is (2 × 3) and (2 × 2 × 5) respectively. As visible, 6 and 20 have only one common prime factor i.e. 2. Hence, the GCF of 6 and 20 is 2.

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GCF of 6 and 20 Examples

Example 1: The product of two numbers is 120. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 120
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 120/2
Therefore, the LCM is 60.
Example 2: Find the greatest number that divides 6 and 20 exactly.

Solution:

The greatest number that divides 6 and 20 exactly is their greatest common factor, i.e. GCF of 6 and 20.
⇒ Factors of 6 and 20:
- Factors of 6 = 1, 2, 3, 6
- Factors of 20 = 1, 2, 4, 5, 10, 20
Therefore, the GCF of 6 and 20 is 2.
Example 3: For two numbers, GCF = 2 and LCM = 60. If one number is 6, find the other number.

Solution:

Given: GCF (x, 6) = 2 and LCM (x, 6) = 60
∵ GCF × LCM = 6 × (x)
⇒ x = (GCF × LCM)/6
⇒ x = (2 × 60)/6
⇒ x = 20
Therefore, the other number is 20.

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FAQs on GCF of 6 and 20

What is the GCF of 6 and 20?

The GCF of 6 and 20 is 2. To calculate the greatest common factor (GCF) of 6 and 20, we need to factor each number (factors of 6 = 1, 2, 3, 6; factors of 20 = 1, 2, 4, 5, 10, 20) and choose the greatest factor that exactly divides both 6 and 20, i.e., 2.

How to Find the GCF of 6 and 20 by Long Division Method?

To find the GCF of 6, 20 using long division method, 20 is divided by 6. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

If the GCF of 20 and 6 is 2, Find its LCM.

GCF(20, 6) × LCM(20, 6) = 20 × 6
Since the GCF of 20 and 6 = 2
⇒ 2 × LCM(20, 6) = 120
Therefore, LCM = 60
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 6 and 20?

There are three commonly used methods to find the GCF of 6 and 20.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the GCF of 6 and 20 by Prime Factorization?

To find the GCF of 6 and 20, we will find the prime factorization of the given numbers, i.e. 6 = 2 × 3; 20 = 2 × 2 × 5.
⇒ Since 2 is the only common prime factor of 6 and 20. Hence, GCF (6, 20) = 2.
☛ What are Prime Numbers?

What is the Relation Between LCM and GCF of 6, 20?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 6 and 20, i.e. GCF × LCM = 6 × 20.

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