GCF that 9 and 12 is the largest feasible number that divides 9 and 12 exactly without any type of remainder. The components of 9 and 12 room 1, 3, 9 and also 1, 2, 3, 4, 6, 12 respectively. There space 3 frequently used methods to uncover the GCF the 9 and 12 - element factorization, long division, and also Euclidean algorithm.

You are watching: Common factors of 9 and 12

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

Answer: GCF of 9 and also 12 is 3.

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Explanation:

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


The methods to discover the GCF that 9 and also 12 are defined below.

Long division MethodPrime administer MethodListing typical Factors

GCF the 9 and 12 by long Division

GCF of 9 and 12 is the divisor the we acquire when the remainder becomes 0 after ~ doing long division repeatedly.

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

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

GCF that 9 and 12 by element Factorization

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

GCF the 9 and 12 through Listing typical Factors

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

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

☛ likewise Check:


GCF of 9 and also 12 Examples


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

Solution:

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


Example 2: uncover the GCF the 9 and also 12, if their LCM is 36.

Solution:

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


Example 3: discover the greatest number that divides 9 and 12 exactly.

Solution:

The greatest number that divides 9 and also 12 specifically is their greatest typical factor, i.e. GCF of 9 and 12.⇒ components of 9 and also 12:

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

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


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FAQs top top GCF the 9 and 12

What is the GCF the 9 and also 12?

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

How to discover the GCF that 9 and also 12 by prime Factorization?

To uncover the GCF that 9 and 12, us will find the element factorization that the offered numbers, i.e. 9 = 3 × 3; 12 = 2 × 2 × 3.⇒ due to the fact that 3 is the only usual prime variable of 9 and also 12. Hence, GCF (9, 12) = 3.☛ element Number

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

The following equation can be offered to to express the relation in between LCM (Least usual Multiple) and GCF of 9 and also 12, i.e. GCF × LCM = 9 × 12.

How to find the GCF that 9 and also 12 through Long department Method?

To find the GCF the 9, 12 using long division method, 12 is separated by 9. The equivalent divisor (3) as soon as remainder equals 0 is taken together GCF.

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

See more: What Is 20 Percent Of 13 Dollars, Calculate 20% Of 13

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 are the techniques to uncover GCF the 9 and 12?

There room three commonly used techniques to uncover the GCF that 9 and 12.