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.

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

Answer: GCF of 3 and 9 is 3.

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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.


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

Listing Common FactorsLong Division MethodPrime Factorization Method

GCF of 3 and 9 by Listing Common Factors

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Factors of 3: 1, 3Factors 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 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

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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 = 27/3Therefore, 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 = 3Therefore, 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, 3Factors 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 DivisionBy Prime FactorizationBy Listing Common Factors

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

GCF(9, 3) × LCM(9, 3) = 9 × 3Since the GCF of 9 and 3 = 3⇒ 3 × LCM(9, 3) = 27Therefore, LCM = 9☛ Greatest Common Factor Calculator

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.

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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.☛ Prime Numbers