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GCF of 17 and 34

GCF of 17 and 34 is the largest possible number that divides 17 and 34 exactly without any remainder. The factors of 17 and 34 are 1, 17 and 1, 2, 17, 34 respectively. There are 3 commonly used methods to find the GCF of 17 and 34 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 17 and 34
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 17 and 34?

Answer: GCF of 17 and 34 is 17.

Explanation:

The GCF of two non-zero integers, x(17) and y(34), is the greatest positive integer m(17) that divides both x(17) and y(34) without any remainder.

Methods to Find GCF of 17 and 34

The methods to find the GCF of 17 and 34 are explained below.

Long Division Method
Listing Common Factors
Prime Factorization Method

GCF of 17 and 34 by Long Division

GCF of 17 and 34 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 34 (larger number) by 17 (smaller number).
Step 2: Since the remainder = 0, the divisor (17) is the GCF of 17 and 34.

The corresponding divisor (17) is the GCF of 17 and 34.

GCF of 17 and 34 by Listing Common Factors

Factors of 17: 1, 17
Factors of 34: 1, 2, 17, 34

There are 2 common factors of 17 and 34, that are 1 and 17. Therefore, the greatest common factor of 17 and 34 is 17.

GCF of 17 and 34 by Prime Factorization

Prime factorization of 17 and 34 is (17) and (2 × 17) respectively. As visible, 17 and 34 have only one common prime factor i.e. 17. Hence, the GCF of 17 and 34 is 17.

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GCF of 17 and 34 Examples

Example 1: Find the greatest number that divides 17 and 34 exactly.

Solution:

The greatest number that divides 17 and 34 exactly is their greatest common factor, i.e. GCF of 17 and 34.
⇒ Factors of 17 and 34:
- Factors of 17 = 1, 17
- Factors of 34 = 1, 2, 17, 34
Therefore, the GCF of 17 and 34 is 17.
Example 2: For two numbers, GCF = 17 and LCM = 34. If one number is 34, find the other number.

Solution:

Given: GCF (y, 34) = 17 and LCM (y, 34) = 34
∵ GCF × LCM = 34 × (y)
⇒ y = (GCF × LCM)/34
⇒ y = (17 × 34)/34
⇒ y = 17
Therefore, the other number is 17.
Example 3: The product of two numbers is 578. If their GCF is 17, what is their LCM?

Solution:

Given: GCF = 17 and product of numbers = 578
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 578/17
Therefore, the LCM is 34.

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FAQs on GCF of 17 and 34

What is the GCF of 17 and 34?

The GCF of 17 and 34 is 17. To calculate the GCF (Greatest Common Factor) of 17 and 34, we need to factor each number (factors of 17 = 1, 17; factors of 34 = 1, 2, 17, 34) and choose the greatest factor that exactly divides both 17 and 34, i.e., 17.

How to Find the GCF of 17 and 34 by Prime Factorization?

To find the GCF of 17 and 34, we will find the prime factorization of the given numbers, i.e. 17 = 17; 34 = 2 × 17.
⇒ Since 17 is the only common prime factor of 17 and 34. Hence, GCF (17, 34) = 17.
☛ Prime Number

How to Find the GCF of 17 and 34 by Long Division Method?

To find the GCF of 17, 34 using long division method, 34 is divided by 17. The corresponding divisor (17) when remainder equals 0 is taken as GCF.

If the GCF of 34 and 17 is 17, Find its LCM.

GCF(34, 17) × LCM(34, 17) = 34 × 17
Since the GCF of 34 and 17 = 17
⇒ 17 × LCM(34, 17) = 578
Therefore, LCM = 34
☛ GCF Calculator

What is the Relation Between LCM and GCF of 17, 34?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 17 and 34, i.e. GCF × LCM = 17 × 34.

What are the Methods to Find GCF of 17 and 34?

There are three commonly used methods to find the GCF of 17 and 34.

By Prime Factorization
By Euclidean Algorithm
By Long Division

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