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GCF of 6 and 7

GCF of 6 and 7 is the largest possible number that divides 6 and 7 exactly without any remainder. The factors of 6 and 7 are 1, 2, 3, 6 and 1, 7 respectively. There are 3 commonly used methods to find the GCF of 6 and 7 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 6 and 7
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 6 and 7?

Answer: GCF of 6 and 7 is 1.

Explanation:

The GCF of two non-zero integers, x(6) and y(7), is the greatest positive integer m(1) that divides both x(6) and y(7) without any remainder.

Methods to Find GCF of 6 and 7

Let's look at the different methods for finding the GCF of 6 and 7.

Using Euclid's Algorithm
Listing Common Factors
Long Division Method

GCF of 6 and 7 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 = 7 and Y = 6

GCF(7, 6) = GCF(6, 7 mod 6) = GCF(6, 1)
GCF(6, 1) = GCF(1, 6 mod 1) = GCF(1, 0)
GCF(1, 0) = 1 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 6 and 7 is 1.

GCF of 6 and 7 by Listing Common Factors

Factors of 6: 1, 2, 3, 6
Factors of 7: 1, 7

Since, 1 is the only common factor between 6 and 7. The Greatest Common Factor of 6 and 7 is 1.

GCF of 6 and 7 by Long Division

GCF of 6 and 7 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 7 (larger number) by 6 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (6) by the remainder (1).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 6 and 7.

☛ Also Check:

GCF of 6 and 7 Examples

Example 1: Find the GCF of 6 and 7, if their LCM is 42.

Solution:

∵ LCM × GCF = 6 × 7
⇒ GCF(6, 7) = (6 × 7)/42 = 1
Therefore, the greatest common factor of 6 and 7 is 1.
Example 2: The product of two numbers is 42. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 42
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 42/1
Therefore, the LCM is 42.
Example 3: Find the greatest number that divides 6 and 7 exactly.

Solution:

The greatest number that divides 6 and 7 exactly is their greatest common factor, i.e. GCF of 6 and 7.
⇒ Factors of 6 and 7:
- Factors of 6 = 1, 2, 3, 6
- Factors of 7 = 1, 7
Therefore, the GCF of 6 and 7 is 1.

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FAQs on GCF of 6 and 7

What is the GCF of 6 and 7?

The GCF of 6 and 7 is 1. To calculate the greatest common factor (GCF) of 6 and 7, we need to factor each number (factors of 6 = 1, 2, 3, 6; factors of 7 = 1, 7) and choose the greatest factor that exactly divides both 6 and 7, i.e., 1.

How to Find the GCF of 6 and 7 by Prime Factorization?

To find the GCF of 6 and 7, we will find the prime factorization of the given numbers, i.e. 6 = 2 × 3; 7 = 7.
⇒ There is no common prime factor for 6 and 7. Hence, GCF (6, 7) = 1.
☛ What are Prime Numbers?

If the GCF of 7 and 6 is 1, Find its LCM.

GCF(7, 6) × LCM(7, 6) = 7 × 6
Since the GCF of 7 and 6 = 1
⇒ 1 × LCM(7, 6) = 42
Therefore, LCM = 42
☛ GCF Calculator

How to Find the GCF of 6 and 7 by Long Division Method?

To find the GCF of 6, 7 using long division method, 7 is divided by 6. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 6, 7?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 6 and 7, i.e. GCF × LCM = 6 × 7.

What are the Methods to Find GCF of 6 and 7?

There are three commonly used methods to find the GCF of 6 and 7.

By Prime Factorization
By Long Division
By Listing Common Factors

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