GCF of 17 and 51
GCF of 17 and 51 is the largest possible number that divides 17 and 51 exactly without any remainder. The factors of 17 and 51 are 1, 17 and 1, 3, 17, 51 respectively. There are 3 commonly used methods to find the GCF of 17 and 51  Euclidean algorithm, prime factorization, and long division.
1.  GCF of 17 and 51 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 17 and 51?
Answer: GCF of 17 and 51 is 17.
Explanation:
The GCF of two nonzero integers, x(17) and y(51), is the greatest positive integer m(17) that divides both x(17) and y(51) without any remainder.
Methods to Find GCF of 17 and 51
The methods to find the GCF of 17 and 51 are explained below.
 Prime Factorization Method
 Using Euclid's Algorithm
 Listing Common Factors
GCF of 17 and 51 by Prime Factorization
Prime factorization of 17 and 51 is (17) and (3 × 17) respectively. As visible, 17 and 51 have only one common prime factor i.e. 17. Hence, the GCF of 17 and 51 is 17.
GCF of 17 and 51 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 = 51 and Y = 17
 GCF(51, 17) = GCF(17, 51 mod 17) = GCF(17, 0)
 GCF(17, 0) = 17 (∵ GCF(X, 0) = X, where X ≠ 0)
Therefore, the value of GCF of 17 and 51 is 17.
GCF of 17 and 51 by Listing Common Factors
 Factors of 17: 1, 17
 Factors of 51: 1, 3, 17, 51
There are 2 common factors of 17 and 51, that are 1 and 17. Therefore, the greatest common factor of 17 and 51 is 17.
☛ Also Check:
 GCF of 90 and 27 = 9
 GCF of 4 and 10 = 2
 GCF of 36 and 40 = 4
 GCF of 40 and 56 = 8
 GCF of 21 and 42 = 21
 GCF of 35 and 63 = 7
 GCF of 45 and 72 = 9
GCF of 17 and 51 Examples

Example 1: The product of two numbers is 867. If their GCF is 17, what is their LCM?
Solution:
Given: GCF = 17 and product of numbers = 867
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 867/17
Therefore, the LCM is 51. 
Example 2: Find the greatest number that divides 17 and 51 exactly.
Solution:
The greatest number that divides 17 and 51 exactly is their greatest common factor, i.e. GCF of 17 and 51.
⇒ Factors of 17 and 51: Factors of 17 = 1, 17
 Factors of 51 = 1, 3, 17, 51
Therefore, the GCF of 17 and 51 is 17.

Example 3: Find the GCF of 17 and 51, if their LCM is 51.
Solution:
∵ LCM × GCF = 17 × 51
⇒ GCF(17, 51) = (17 × 51)/51 = 17
Therefore, the greatest common factor of 17 and 51 is 17.
FAQs on GCF of 17 and 51
What is the GCF of 17 and 51?
The GCF of 17 and 51 is 17. To calculate the GCF of 17 and 51, we need to factor each number (factors of 17 = 1, 17; factors of 51 = 1, 3, 17, 51) and choose the greatest factor that exactly divides both 17 and 51, i.e., 17.
What are the Methods to Find GCF of 17 and 51?
There are three commonly used methods to find the GCF of 17 and 51.
 By Prime Factorization
 By Long Division
 By Euclidean Algorithm
If the GCF of 51 and 17 is 17, Find its LCM.
GCF(51, 17) × LCM(51, 17) = 51 × 17
Since the GCF of 51 and 17 = 17
⇒ 17 × LCM(51, 17) = 867
Therefore, LCM = 51
☛ Greatest Common Factor Calculator
How to Find the GCF of 17 and 51 by Prime Factorization?
To find the GCF of 17 and 51, we will find the prime factorization of the given numbers, i.e. 17 = 17; 51 = 3 × 17.
⇒ Since 17 is the only common prime factor of 17 and 51. Hence, GCF (17, 51) = 17.
☛ Prime Number
How to Find the GCF of 17 and 51 by Long Division Method?
To find the GCF of 17, 51 using long division method, 51 is divided by 17. The corresponding divisor (17) when remainder equals 0 is taken as GCF.
What is the Relation Between LCM and GCF of 17, 51?
The following equation can be used to express the relation between LCM and GCF of 17 and 51, i.e. GCF × LCM = 17 × 51.
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