GCF of 9 and 12 is the largest feasible number the divides 9 and also 12 exactly without any remainder. The determinants of 9 and 12 are 1, 3, 9 and also 1, 2, 3, 4, 6, 12 respectively. There room 3 typically used methods to uncover the GCF of 9 and 12 - prime factorization, long division, and Euclidean algorithm.

You are watching: What is the greatest common factor of 9 and 12?

1.GCF of 9 and also 12
2.List that Methods
3.Solved Examples
4.FAQs

Answer: GCF that 9 and also 12 is 3.

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Explanation:

The GCF of two non-zero integers, x(9) and y(12), is the greatest positive essence m(3) the divides both x(9) and y(12) without any kind of remainder.


The techniques to find the GCF that 9 and also 12 are explained below.

Long department MethodPrime administrate MethodListing typical Factors

GCF the 9 and 12 by long Division

GCF the 9 and also 12 is the divisor the we get when the remainder becomes 0 ~ doing long department repeatedly.

Step 2: because the remainder ≠ 0, we will certainly divide the divisor of step 1 (9) by the remainder (3).Step 3: Repeat this procedure until the remainder = 0.

The matching divisor (3) is the GCF of 9 and 12.

GCF of 9 and also 12 by element Factorization

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Prime administer of 9 and also 12 is (3 × 3) and also (2 × 2 × 3) respectively. Together visible, 9 and 12 have only one typical prime aspect i.e. 3. Hence, the GCF that 9 and 12 is 3.

GCF of 9 and also 12 through Listing usual Factors

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Factors the 9: 1, 3, 9Factors the 12: 1, 2, 3, 4, 6, 12

There space 2 common factors that 9 and also 12, that space 1 and also 3. Therefore, the greatest common factor that 9 and also 12 is 3.

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GCF that 9 and also 12 Examples


Example 1: The product of 2 numbers is 108. If your GCF is 3, what is your LCM?

Solution:

Given: GCF = 3 and also product of numbers = 108∵ LCM × GCF = product the numbers⇒ LCM = Product/GCF = 108/3Therefore, the LCM is 36.


Example 2: discover the GCF of 9 and 12, if their LCM is 36.

Solution:

∵ LCM × GCF = 9 × 12⇒ GCF(9, 12) = (9 × 12)/36 = 3Therefore, the greatest usual factor of 9 and also 12 is 3.


Example 3: find the greatest number the divides 9 and also 12 exactly.

Solution:

The best number the divides 9 and 12 precisely is their greatest common factor, i.e. GCF the 9 and 12.⇒ factors of 9 and also 12:

Factors that 9 = 1, 3, 9Factors of 12 = 1, 2, 3, 4, 6, 12

Therefore, the GCF that 9 and 12 is 3.


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FAQs on GCF that 9 and also 12

What is the GCF that 9 and also 12?

The GCF that 9 and also 12 is 3. To calculation the GCF (Greatest usual Factor) of 9 and 12, we require to element each number (factors of 9 = 1, 3, 9; factors of 12 = 1, 2, 3, 4, 6, 12) and choose the greatest variable that exactly divides both 9 and 12, i.e., 3.

How to find the GCF that 9 and 12 by element Factorization?

To discover the GCF the 9 and 12, we will find the prime factorization that the offered numbers, i.e. 9 = 3 × 3; 12 = 2 × 2 × 3.⇒ because 3 is the only typical prime aspect of 9 and also 12. Hence, GCF (9, 12) = 3.☛ prime Number

What is the Relation between LCM and also GCF of 9, 12?

The complying with equation deserve to be supplied to express the relation between LCM (Least common Multiple) and GCF of 9 and also 12, i.e. GCF × LCM = 9 × 12.

How to discover the GCF the 9 and 12 by Long department Method?

To find the GCF that 9, 12 using long division method, 12 is separated by 9. The corresponding divisor (3) once remainder amounts to 0 is taken as GCF.

If the GCF the 12 and 9 is 3, uncover its LCM.

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GCF(12, 9) × LCM(12, 9) = 12 × 9Since the GCF of 12 and 9 = 3⇒ 3 × LCM(12, 9) = 108Therefore, LCM = 36☛ Greatest usual Factor Calculator

What are the approaches to discover GCF that 9 and also 12?

There are three commonly used techniques to uncover the GCF of 9 and also 12.