GCF of 14 and 63
GCF of 14 and 63 is the largest possible number that divides 14 and 63 exactly without any remainder. The factors of 14 and 63 are 1, 2, 7, 14 and 1, 3, 7, 9, 21, 63 respectively. There are 3 commonly used methods to find the GCF of 14 and 63  Euclidean algorithm, prime factorization, and long division.
1.  GCF of 14 and 63 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 14 and 63?
Answer: GCF of 14 and 63 is 7.
Explanation:
The GCF of two nonzero integers, x(14) and y(63), is the greatest positive integer m(7) that divides both x(14) and y(63) without any remainder.
Methods to Find GCF of 14 and 63
Let's look at the different methods for finding the GCF of 14 and 63.
 Prime Factorization Method
 Listing Common Factors
 Long Division Method
GCF of 14 and 63 by Prime Factorization
Prime factorization of 14 and 63 is (2 × 7) and (3 × 3 × 7) respectively. As visible, 14 and 63 have only one common prime factor i.e. 7. Hence, the GCF of 14 and 63 is 7.
GCF of 14 and 63 by Listing Common Factors
 Factors of 14: 1, 2, 7, 14
 Factors of 63: 1, 3, 7, 9, 21, 63
There are 2 common factors of 14 and 63, that are 1 and 7. Therefore, the greatest common factor of 14 and 63 is 7.
GCF of 14 and 63 by Long Division
GCF of 14 and 63 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 63 (larger number) by 14 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (14) by the remainder (7).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (7) is the GCF of 14 and 63.
☛ Also Check:
 GCF of 7 and 28 = 7
 GCF of 15 and 36 = 3
 GCF of 56 and 49 = 7
 GCF of 34 and 85 = 17
 GCF of 36 and 81 = 9
 GCF of 42 and 70 = 14
 GCF of 84 and 96 = 12
GCF of 14 and 63 Examples

Example 1: Find the greatest number that divides 14 and 63 exactly.
Solution:
The greatest number that divides 14 and 63 exactly is their greatest common factor, i.e. GCF of 14 and 63.
⇒ Factors of 14 and 63: Factors of 14 = 1, 2, 7, 14
 Factors of 63 = 1, 3, 7, 9, 21, 63
Therefore, the GCF of 14 and 63 is 7.

Example 2: The product of two numbers is 882. If their GCF is 7, what is their LCM?
Solution:
Given: GCF = 7 and product of numbers = 882
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 882/7
Therefore, the LCM is 126. 
Example 3: For two numbers, GCF = 7 and LCM = 126. If one number is 63, find the other number.
Solution:
Given: GCF (z, 63) = 7 and LCM (z, 63) = 126
∵ GCF × LCM = 63 × (z)
⇒ z = (GCF × LCM)/63
⇒ z = (7 × 126)/63
⇒ z = 14
Therefore, the other number is 14.
FAQs on GCF of 14 and 63
What is the GCF of 14 and 63?
The GCF of 14 and 63 is 7. To calculate the GCF (Greatest Common Factor) of 14 and 63, we need to factor each number (factors of 14 = 1, 2, 7, 14; factors of 63 = 1, 3, 7, 9, 21, 63) and choose the greatest factor that exactly divides both 14 and 63, i.e., 7.
What are the Methods to Find GCF of 14 and 63?
There are three commonly used methods to find the GCF of 14 and 63.
 By Listing Common Factors
 By Long Division
 By Prime Factorization
If the GCF of 63 and 14 is 7, Find its LCM.
GCF(63, 14) × LCM(63, 14) = 63 × 14
Since the GCF of 63 and 14 = 7
⇒ 7 × LCM(63, 14) = 882
Therefore, LCM = 126
☛ GCF Calculator
How to Find the GCF of 14 and 63 by Long Division Method?
To find the GCF of 14, 63 using long division method, 63 is divided by 14. The corresponding divisor (7) when remainder equals 0 is taken as GCF.
What is the Relation Between LCM and GCF of 14, 63?
The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 14 and 63, i.e. GCF × LCM = 14 × 63.
How to Find the GCF of 14 and 63 by Prime Factorization?
To find the GCF of 14 and 63, we will find the prime factorization of the given numbers, i.e. 14 = 2 × 7; 63 = 3 × 3 × 7.
⇒ Since 7 is the only common prime factor of 14 and 63. Hence, GCF (14, 63) = 7.
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