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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 non-zero 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.

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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.

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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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