GCF that 9 and 12 is the largest possible number that divides 9 and 12 exactly without any remainder. The factors of 9 and also 12 room 1, 3, 9 and 1, 2, 3, 4, 6, 12 respectively. There are 3 generally used techniques to discover the GCF of 9 and also 12 - element factorization, long division, and also Euclidean algorithm.

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

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

Answer: GCF that 9 and 12 is 3.

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Explanation:

The GCF of 2 non-zero integers, x(9) and y(12), is the greatest positive creature m(3) that divides both x(9) and also y(12) without any type of remainder.


The approaches to uncover the GCF the 9 and 12 are explained below.

Long department MethodPrime administer MethodListing typical Factors

GCF of 9 and 12 by lengthy Division

GCF of 9 and 12 is the divisor that we gain when the remainder i do not care 0 ~ doing long division repeatedly.

Step 2: since the remainder ≠ 0, we will certainly divide the divisor of action 1 (9) through the remainder (3).Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the GCF that 9 and also 12.

GCF of 9 and 12 by element Factorization

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Prime administrate of 9 and also 12 is (3 × 3) and also (2 × 2 × 3) respectively. As visible, 9 and 12 have actually only one usual prime aspect i.e. 3. Hence, the GCF of 9 and 12 is 3.

GCF that 9 and 12 by Listing typical Factors

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

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

☛ likewise Check:


GCF that 9 and 12 Examples


Example 1: The product of two 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 that numbers⇒ LCM = Product/GCF = 108/3Therefore, the LCM is 36.


Example 2: find the GCF the 9 and 12, if your LCM is 36.

Solution:

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


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

Solution:

The best number the divides 9 and 12 exactly is your greatest usual factor, i.e. GCF the 9 and also 12.⇒ components of 9 and 12:

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

Therefore, the GCF of 9 and also 12 is 3.


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FAQs top top GCF the 9 and 12

What is the GCF that 9 and 12?

The GCF that 9 and also 12 is 3. To calculate the GCF (Greatest common Factor) the 9 and also 12, we require to factor each number (factors that 9 = 1, 3, 9; components of 12 = 1, 2, 3, 4, 6, 12) and choose the greatest aspect that precisely divides both 9 and 12, i.e., 3.

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

To discover the GCF the 9 and also 12, us will find the prime factorization that the given numbers, i.e. 9 = 3 × 3; 12 = 2 × 2 × 3.⇒ since 3 is the only usual prime aspect of 9 and also 12. Hence, GCF (9, 12) = 3.☛ element Number

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

The adhering to equation have the right to be supplied to refer the relation between LCM (Least typical Multiple) and GCF the 9 and also 12, i.e. GCF × LCM = 9 × 12.

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

To find the GCF the 9, 12 utilizing long department method, 12 is split by 9. The equivalent divisor (3) once remainder equates to 0 is taken together GCF.

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

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

What space the techniques to uncover GCF the 9 and 12?

There room three typically used approaches to discover the GCF of 9 and also 12.