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GCF of 7 and 14

GCF of 7 and 14 is the largest possible number that divides 7 and 14 exactly without any remainder. The factors of 7 and 14 are 1, 7 and 1, 2, 7, 14 respectively. There are 3 commonly used methods to find the GCF of 7 and 14 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 7 and 14
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 7 and 14?

Answer: GCF of 7 and 14 is 7.

Explanation:

The GCF of two non-zero integers, x(7) and y(14), is the greatest positive integer m(7) that divides both x(7) and y(14) without any remainder.

Methods to Find GCF of 7 and 14

Let's look at the different methods for finding the GCF of 7 and 14.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

GCF of 7 and 14 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 = 14 and Y = 7

GCF(14, 7) = GCF(7, 14 mod 7) = GCF(7, 0)
GCF(7, 0) = 7 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 7 and 14 is 7.

GCF of 7 and 14 by Long Division

GCF of 7 and 14 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 14 (larger number) by 7 (smaller number).
Step 2: Since the remainder = 0, the divisor (7) is the GCF of 7 and 14.

The corresponding divisor (7) is the GCF of 7 and 14.

GCF of 7 and 14 by Listing Common Factors

Factors of 7: 1, 7
Factors of 14: 1, 2, 7, 14

There are 2 common factors of 7 and 14, that are 1 and 7. Therefore, the greatest common factor of 7 and 14 is 7.

☛ Also Check:

GCF of 7 and 14 Examples

Example 1: For two numbers, GCF = 7 and LCM = 14. If one number is 7, find the other number.

Solution:

Given: GCF (x, 7) = 7 and LCM (x, 7) = 14
∵ GCF × LCM = 7 × (x)
⇒ x = (GCF × LCM)/7
⇒ x = (7 × 14)/7
⇒ x = 14
Therefore, the other number is 14.
Example 2: Find the GCF of 7 and 14, if their LCM is 14.

Solution:

∵ LCM × GCF = 7 × 14
⇒ GCF(7, 14) = (7 × 14)/14 = 7
Therefore, the greatest common factor of 7 and 14 is 7.
Example 3: The product of two numbers is 98. If their GCF is 7, what is their LCM?

Solution:

Given: GCF = 7 and product of numbers = 98
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 98/7
Therefore, the LCM is 14.

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FAQs on GCF of 7 and 14

What is the GCF of 7 and 14?

The GCF of 7 and 14 is 7. To calculate the greatest common factor (GCF) of 7 and 14, we need to factor each number (factors of 7 = 1, 7; factors of 14 = 1, 2, 7, 14) and choose the greatest factor that exactly divides both 7 and 14, i.e., 7.

If the GCF of 14 and 7 is 7, Find its LCM.

GCF(14, 7) × LCM(14, 7) = 14 × 7
Since the GCF of 14 and 7 = 7
⇒ 7 × LCM(14, 7) = 98
Therefore, LCM = 14
☛ GCF Calculator

What is the Relation Between LCM and GCF of 7, 14?

The following equation can be used to express the relation between Least Common Multiple and GCF of 7 and 14, i.e. GCF × LCM = 7 × 14.

How to Find the GCF of 7 and 14 by Prime Factorization?

To find the GCF of 7 and 14, we will find the prime factorization of the given numbers, i.e. 7 = 7; 14 = 2 × 7.
⇒ Since 7 is the only common prime factor of 7 and 14. Hence, GCF (7, 14) = 7.
☛ What are Prime Numbers?

How to Find the GCF of 7 and 14 by Long Division Method?

To find the GCF of 7, 14 using long division method, 14 is divided by 7. The corresponding divisor (7) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 7 and 14?

There are three commonly used methods to find the GCF of 7 and 14.

By Prime Factorization
By Listing Common Factors
By Long Division

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