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GCF of 13 and 17

GCF of 13 and 17 is the largest possible number that divides 13 and 17 exactly without any remainder. The factors of 13 and 17 are 1, 13 and 1, 17 respectively. There are 3 commonly used methods to find the GCF of 13 and 17 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 13 and 17
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 13 and 17?

Answer: GCF of 13 and 17 is 1.

Explanation:

The GCF of two non-zero integers, x(13) and y(17), is the greatest positive integer m(1) that divides both x(13) and y(17) without any remainder.

Methods to Find GCF of 13 and 17

The methods to find the GCF of 13 and 17 are explained below.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

GCF of 13 and 17 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 = 17 and Y = 13

GCF(17, 13) = GCF(13, 17 mod 13) = GCF(13, 4)
GCF(13, 4) = GCF(4, 13 mod 4) = GCF(4, 1)
GCF(4, 1) = 1 (∵ GCF(X, 1) = 1)

Therefore, the value of GCF of 13 and 17 is 1.

GCF of 13 and 17 by Long Division

GCF of 13 and 17 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 17 (larger number) by 13 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (13) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 13 and 17.

GCF of 13 and 17 by Listing Common Factors

Factors of 13: 1, 13
Factors of 17: 1, 17

Since, 1 is the only common factor between 13 and 17. The Greatest Common Factor of 13 and 17 is 1.

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GCF of 13 and 17 Examples

Example 1: Find the greatest number that divides 13 and 17 exactly.

Solution:

The greatest number that divides 13 and 17 exactly is their greatest common factor, i.e. GCF of 13 and 17.
⇒ Factors of 13 and 17:
- Factors of 13 = 1, 13
- Factors of 17 = 1, 17
Therefore, the GCF of 13 and 17 is 1.
Example 2: The product of two numbers is 221. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 221
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 221/1
Therefore, the LCM is 221.
Example 3: Find the GCF of 13 and 17, if their LCM is 221.

Solution:

∵ LCM × GCF = 13 × 17
⇒ GCF(13, 17) = (13 × 17)/221 = 1
Therefore, the greatest common factor of 13 and 17 is 1.

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FAQs on GCF of 13 and 17

What is the GCF of 13 and 17?

The GCF of 13 and 17 is 1. To calculate the greatest common factor of 13 and 17, we need to factor each number (factors of 13 = 1, 13; factors of 17 = 1, 17) and choose the greatest factor that exactly divides both 13 and 17, i.e., 1.

What is the Relation Between LCM and GCF of 13, 17?

The following equation can be used to express the relation between LCM and GCF of 13 and 17, i.e. GCF × LCM = 13 × 17.

How to Find the GCF of 13 and 17 by Prime Factorization?

To find the GCF of 13 and 17, we will find the prime factorization of the given numbers, i.e. 13 = 13; 17 = 17.
⇒ There is no common prime factor for 13 and 17. Hence, GCF (13, 17) = 1.
☛ What is a Prime Number?

What are the Methods to Find GCF of 13 and 17?

There are three commonly used methods to find the GCF of 13 and 17.

By Prime Factorization
By Listing Common Factors
By Long Division

If the GCF of 17 and 13 is 1, Find its LCM.

GCF(17, 13) × LCM(17, 13) = 17 × 13
Since the GCF of 17 and 13 = 1
⇒ 1 × LCM(17, 13) = 221
Therefore, LCM = 221
☛ GCF Calculator

How to Find the GCF of 13 and 17 by Long Division Method?

To find the GCF of 13, 17 using long division method, 17 is divided by 13. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

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