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GCF of 8 and 13

GCF of 8 and 13 is the largest possible number that divides 8 and 13 exactly without any remainder. The factors of 8 and 13 are 1, 2, 4, 8 and 1, 13 respectively. There are 3 commonly used methods to find the GCF of 8 and 13 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 8 and 13
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 8 and 13?

Answer: GCF of 8 and 13 is 1.

Explanation:

The GCF of two non-zero integers, x(8) and y(13), is the greatest positive integer m(1) that divides both x(8) and y(13) without any remainder.

Methods to Find GCF of 8 and 13

Let's look at the different methods for finding the GCF of 8 and 13.

Long Division Method
Using Euclid's Algorithm
Prime Factorization Method

GCF of 8 and 13 by Long Division

GCF of 8 and 13 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 13 (larger number) by 8 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (8) by the remainder (5).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 8 and 13.

GCF of 8 and 13 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 = 13 and Y = 8

GCF(13, 8) = GCF(8, 13 mod 8) = GCF(8, 5)
GCF(8, 5) = GCF(5, 8 mod 5) = GCF(5, 3)
GCF(5, 3) = GCF(3, 5 mod 3) = GCF(3, 2)
GCF(3, 2) = GCF(2, 3 mod 2) = GCF(2, 1)
GCF(2, 1) = 1 (∵ GCF(X, 1) = 1)

Therefore, the value of GCF of 8 and 13 is 1.

GCF of 8 and 13 by Prime Factorization

Prime factorization of 8 and 13 is (2 × 2 × 2) and (13) respectively. As visible, there are no common prime factors between 8 and 13, i.e. they are coprime. Hence, the GCF of 8 and 13 will be 1.

☛ Also Check:

GCF of 8 and 13 Examples

Example 1: The product of two numbers is 104. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 104
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 104/1
Therefore, the LCM is 104.
Example 2: Find the GCF of 8 and 13, if their LCM is 104.

Solution:

∵ LCM × GCF = 8 × 13
⇒ GCF(8, 13) = (8 × 13)/104 = 1
Therefore, the greatest common factor of 8 and 13 is 1.
Example 3: Find the greatest number that divides 8 and 13 exactly.

Solution:

The greatest number that divides 8 and 13 exactly is their greatest common factor, i.e. GCF of 8 and 13.
⇒ Factors of 8 and 13:
- Factors of 8 = 1, 2, 4, 8
- Factors of 13 = 1, 13
Therefore, the GCF of 8 and 13 is 1.

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FAQs on GCF of 8 and 13

What is the GCF of 8 and 13?

The GCF of 8 and 13 is 1. To calculate the greatest common factor of 8 and 13, we need to factor each number (factors of 8 = 1, 2, 4, 8; factors of 13 = 1, 13) and choose the greatest factor that exactly divides both 8 and 13, i.e., 1.

How to Find the GCF of 8 and 13 by Long Division Method?

To find the GCF of 8, 13 using long division method, 13 is divided by 8. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 8, 13?

The following equation can be used to express the relation between LCM and GCF of 8 and 13, i.e. GCF × LCM = 8 × 13.

How to Find the GCF of 8 and 13 by Prime Factorization?

To find the GCF of 8 and 13, we will find the prime factorization of the given numbers, i.e. 8 = 2 × 2 × 2; 13 = 13.
⇒ There is no common prime factor for 8 and 13. Hence, GCF (8, 13) = 1.
☛ Prime Numbers

If the GCF of 13 and 8 is 1, Find its LCM.

GCF(13, 8) × LCM(13, 8) = 13 × 8
Since the GCF of 13 and 8 = 1
⇒ 1 × LCM(13, 8) = 104
Therefore, LCM = 104
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 8 and 13?

There are three commonly used methods to find the GCF of 8 and 13.

By Listing Common Factors
By Long Division
By Prime Factorization

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