GCF that 3 and also 12 is the largest possible number that divides 3 and also 12 specifically without any kind of remainder. The determinants of 3 and 12 room 1, 3 and 1, 2, 3, 4, 6, 12 respectively. There space 3 typically used techniques to find the GCF the 3 and also 12 - long division, Euclidean algorithm, and prime factorization.

You are watching: What is the gcf of 3 and 12

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

Answer: GCF the 3 and 12 is 3.

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Explanation:

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


The techniques to find the GCF the 3 and 12 are defined below.

Listing common FactorsLong division MethodPrime administer Method

GCF that 3 and 12 by Listing usual Factors

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

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

GCF of 3 and 12 by long Division

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GCF that 3 and also 12 is the divisor the we get when the remainder becomes 0 ~ doing long division repeatedly.

Step 2: since the remainder = 0, the divisor (3) is the GCF of 3 and 12.

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

GCF the 3 and also 12 by element Factorization

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

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GCF that 3 and also 12 Examples


Example 1: discover the greatest number the divides 3 and 12 exactly.

Solution:

The best number the divides 3 and 12 specifically is their greatest common factor, i.e. GCF the 3 and 12.⇒ determinants of 3 and 12:

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

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


Example 2: uncover the GCF of 3 and 12, if your LCM is 12.

Solution:

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


Example 3: For two numbers, GCF = 3 and also LCM = 12. If one number is 3, discover the other number.

Solution:

Given: GCF (x, 3) = 3 and LCM (x, 3) = 12∵ GCF × LCM = 3 × (x)⇒ x = (GCF × LCM)/3⇒ x = (3 × 12)/3⇒ x = 12Therefore, the other number is 12.


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FAQs on GCF of 3 and 12

What is the GCF the 3 and also 12?

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

What is the Relation between LCM and GCF of 3, 12?

The adhering to equation have the right to be used to express the relation between LCM and also GCF that 3 and 12, i.e. GCF × LCM = 3 × 12.

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

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

What space the techniques to uncover GCF of 3 and also 12?

There space three commonly used methods to find the GCF of 3 and also 12.

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By element FactorizationBy lengthy DivisionBy Listing typical Factors

How to find the GCF the 3 and also 12 by prime Factorization?

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

How to find the GCF the 3 and also 12 by Long department Method?

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