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GCF of 8 and 9

GCF of 8 and 9 is the largest possible number that divides 8 and 9 exactly without any remainder. The factors of 8 and 9 are 1, 2, 4, 8 and 1, 3, 9 respectively. There are 3 commonly used methods to find the GCF of 8 and 9 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 8 and 9
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 8 and 9?

Answer: GCF of 8 and 9 is 1.

Explanation:

The GCF of two non-zero integers, x(8) and y(9), is the greatest positive integer m(1) that divides both x(8) and y(9) without any remainder.

Methods to Find GCF of 8 and 9

The methods to find the GCF of 8 and 9 are explained below.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 8 and 9 by Prime Factorization

Prime factorization of 8 and 9 is (2 × 2 × 2) and (3 × 3) respectively. As visible, there are no common prime factors between 8 and 9, i.e. they are coprime. Hence, the GCF of 8 and 9 will be 1.

GCF of 8 and 9 by Listing Common Factors

Factors of 8: 1, 2, 4, 8
Factors of 9: 1, 3, 9

Since, 1 is the only common factor between 8 and 9. The Greatest Common Factor of 8 and 9 is 1.

GCF of 8 and 9 by Long Division

GCF of 8 and 9 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 9 (larger number) by 8 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (8) by the remainder (1).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 8 and 9.

☛ Also Check:

GCF of 8 and 9 Examples

Example 1: For two numbers, GCF = 1 and LCM = 72. If one number is 9, find the other number.

Solution:

Given: GCF (z, 9) = 1 and LCM (z, 9) = 72
∵ GCF × LCM = 9 × (z)
⇒ z = (GCF × LCM)/9
⇒ z = (1 × 72)/9
⇒ z = 8
Therefore, the other number is 8.
Example 2: The product of two numbers is 72. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 72
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 72/1
Therefore, the LCM is 72.
Example 3: Find the greatest number that divides 8 and 9 exactly.

Solution:

The greatest number that divides 8 and 9 exactly is their greatest common factor, i.e. GCF of 8 and 9.
⇒ Factors of 8 and 9:
- Factors of 8 = 1, 2, 4, 8
- Factors of 9 = 1, 3, 9
Therefore, the GCF of 8 and 9 is 1.

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FAQs on GCF of 8 and 9

What is the GCF of 8 and 9?

The GCF of 8 and 9 is 1. To calculate the GCF (Greatest Common Factor) of 8 and 9, we need to factor each number (factors of 8 = 1, 2, 4, 8; factors of 9 = 1, 3, 9) and choose the greatest factor that exactly divides both 8 and 9, i.e., 1.

What is the Relation Between LCM and GCF of 8, 9?

The following equation can be used to express the relation between LCM and GCF of 8 and 9, i.e. GCF × LCM = 8 × 9.

How to Find the GCF of 8 and 9 by Prime Factorization?

To find the GCF of 8 and 9, we will find the prime factorization of the given numbers, i.e. 8 = 2 × 2 × 2; 9 = 3 × 3.
⇒ There is no common prime factor for 8 and 9. Hence, GCF (8, 9) = 1.
☛ Prime Numbers

If the GCF of 9 and 8 is 1, Find its LCM.

GCF(9, 8) × LCM(9, 8) = 9 × 8
Since the GCF of 9 and 8 = 1
⇒ 1 × LCM(9, 8) = 72
Therefore, LCM = 72
☛ GCF Calculator

What are the Methods to Find GCF of 8 and 9?

There are three commonly used methods to find the GCF of 8 and 9.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the GCF of 8 and 9 by Long Division Method?

To find the GCF of 8, 9 using long division method, 9 is divided by 8. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

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