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 nonzero 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 16 and 24 = 8
 GCF of 15 and 45 = 15
 GCF of 25 and 90 = 5
 GCF of 25 and 45 = 5
 GCF of 21 and 35 = 7
 GCF of 60 and 84 = 12
 GCF of 72 and 96 = 24
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.
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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