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GCF of 3 and 9

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

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

What is GCF of 3 and 9?

Answer: GCF of 3 and 9 is 3.

Explanation:

The GCF of two non-zero integers, x(3) and y(9), is the greatest positive integer m(3) that divides both x(3) and y(9) without any remainder.

Methods to Find GCF of 3 and 9

The methods to find the GCF of 3 and 9 are explained below.

Listing Common Factors
Long Division Method
Prime Factorization Method

GCF of 3 and 9 by Listing Common Factors

Factors of 3: 1, 3
Factors of 9: 1, 3, 9

There are 2 common factors of 3 and 9, that are 1 and 3. Therefore, the greatest common factor of 3 and 9 is 3.

GCF of 3 and 9 by Long Division

GCF of 3 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 3 (smaller number).
Step 2: Since the remainder = 0, the divisor (3) is the GCF of 3 and 9.

The corresponding divisor (3) is the GCF of 3 and 9.

GCF of 3 and 9 by Prime Factorization

Prime factorization of 3 and 9 is (3) and (3 × 3) respectively. As visible, 3 and 9 have only one common prime factor i.e. 3. Hence, the GCF of 3 and 9 is 3.

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GCF of 3 and 9 Examples

Example 1: The product of two numbers is 27. If their GCF is 3, what is their LCM?

Solution:

Given: GCF = 3 and product of numbers = 27
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 27/3
Therefore, the LCM is 9.
Example 2: Find the GCF of 3 and 9, if their LCM is 9.

Solution:

∵ LCM × GCF = 3 × 9
⇒ GCF(3, 9) = (3 × 9)/9 = 3
Therefore, the greatest common factor of 3 and 9 is 3.
Example 3: Find the greatest number that divides 3 and 9 exactly.

Solution:

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

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FAQs on GCF of 3 and 9

What is the GCF of 3 and 9?

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

What are the Methods to Find GCF of 3 and 9?

There are three commonly used methods to find the GCF of 3 and 9.

By Long Division
By Prime Factorization
By Listing Common Factors

If the GCF of 9 and 3 is 3, Find its LCM.

GCF(9, 3) × LCM(9, 3) = 9 × 3
Since the GCF of 9 and 3 = 3
⇒ 3 × LCM(9, 3) = 27
Therefore, LCM = 9
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What is the Relation Between LCM and GCF of 3, 9?

The following equation can be used to express the relation between Least Common Multiple and GCF of 3 and 9, i.e. GCF × LCM = 3 × 9.

How to Find the GCF of 3 and 9 by Long Division Method?

To find the GCF of 3, 9 using long division method, 9 is divided by 3. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

How to Find the GCF of 3 and 9 by Prime Factorization?

To find the GCF of 3 and 9, we will find the prime factorization of the given numbers, i.e. 3 = 3; 9 = 3 × 3.
⇒ Since 3 is the only common prime factor of 3 and 9. Hence, GCF (3, 9) = 3.
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