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GCF of 2 and 7

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

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

What is GCF of 2 and 7?

Answer: GCF of 2 and 7 is 1.

Explanation:

The GCF of two non-zero integers, x(2) and y(7), is the greatest positive integer m(1) that divides both x(2) and y(7) without any remainder.

Methods to Find GCF of 2 and 7

The methods to find the GCF of 2 and 7 are explained below.

Listing Common Factors
Using Euclid's Algorithm
Prime Factorization Method

GCF of 2 and 7 by Listing Common Factors

Factors of 2: 1, 2
Factors of 7: 1, 7

Since, 1 is the only common factor between 2 and 7. The Greatest Common Factor of 2 and 7 is 1.

GCF of 2 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 = 2

GCF(7, 2) = GCF(2, 7 mod 2) = GCF(2, 1)
GCF(2, 1) = GCF(1, 2 mod 1) = GCF(1, 0)
GCF(1, 0) = 1 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 2 and 7 is 1.

GCF of 2 and 7 by Prime Factorization

Prime factorization of 2 and 7 is (2) and (7) respectively. As visible, there are no common prime factors between 2 and 7, i.e. they are co-prime. Hence, the GCF of 2 and 7 will be 1.

☛ Also Check:

GCF of 2 and 7 Examples

Example 1: For two numbers, GCF = 1 and LCM = 14. If one number is 2, find the other number.

Solution:

Given: GCF (y, 2) = 1 and LCM (y, 2) = 14
∵ GCF × LCM = 2 × (y)
⇒ y = (GCF × LCM)/2
⇒ y = (1 × 14)/2
⇒ y = 7
Therefore, the other number is 7.
Example 2: Find the greatest number that divides 2 and 7 exactly.

Solution:

The greatest number that divides 2 and 7 exactly is their greatest common factor, i.e. GCF of 2 and 7.
⇒ Factors of 2 and 7:
- Factors of 2 = 1, 2
- Factors of 7 = 1, 7
Therefore, the GCF of 2 and 7 is 1.
Example 3: Find the GCF of 2 and 7, if their LCM is 14.

Solution:

∵ LCM × GCF = 2 × 7
⇒ GCF(2, 7) = (2 × 7)/14 = 1
Therefore, the greatest common factor of 2 and 7 is 1.

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FAQs on GCF of 2 and 7

What is the GCF of 2 and 7?

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

If the GCF of 7 and 2 is 1, Find its LCM.

GCF(7, 2) × LCM(7, 2) = 7 × 2
Since the GCF of 7 and 2 = 1
⇒ 1 × LCM(7, 2) = 14
Therefore, LCM = 14
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 2 and 7?

There are three commonly used methods to find the GCF of 2 and 7.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the GCF of 2 and 7 by Prime Factorization?

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

How to Find the GCF of 2 and 7 by Long Division Method?

To find the GCF of 2, 7 using long division method, 7 is divided by 2. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 2, 7?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 2 and 7, i.e. GCF × LCM = 2 × 7.

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