GCF the 12 and 48 is the largest feasible number the divides 12 and 48 exactly without any type of remainder. The determinants of 12 and also 48 room 1, 2, 3, 4, 6, 12 and also 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 respectively. There room 3 generally used methods to find the GCF the 12 and also 48 - Euclidean algorithm, long division, and prime factorization.

You are watching: Greatest common factor of 12 and 48

1.GCF the 12 and also 48
2.List the Methods
3.Solved Examples
4.FAQs

Answer: GCF the 12 and 48 is 12.

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Explanation:

The GCF of 2 non-zero integers, x(12) and y(48), is the best positive creature m(12) the divides both x(12) and also y(48) without any type of remainder.


Let's look at the various methods because that finding the GCF the 12 and 48.

Using Euclid's AlgorithmListing typical FactorsLong department Method

GCF of 12 and 48 by Euclidean Algorithm

As every the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)where X > Y and also mod is the modulo operator.

Here X = 48 and Y = 12

GCF(48, 12) = GCF(12, 48 mod 12) = GCF(12, 0)GCF(12, 0) = 12 (∵ GCF(X, 0) = |X|, wherein X ≠ 0)

Therefore, the value of GCF that 12 and 48 is 12.

GCF that 12 and also 48 by Listing typical Factors

Factors that 12: 1, 2, 3, 4, 6, 12Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

There room 6 usual factors of 12 and 48, that space 1, 2, 3, 4, 6, and 12. Therefore, the greatest common factor that 12 and also 48 is 12.

GCF that 12 and 48 by long Division

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GCF of 12 and also 48 is the divisor the we obtain when the remainder becomes 0 after doing long department repeatedly.

Step 2: due to the fact that the remainder = 0, the divisor (12) is the GCF the 12 and also 48.

The corresponding divisor (12) is the GCF the 12 and also 48.

☛ likewise Check:


GCF the 12 and also 48 Examples


Example 1: The product of two numbers is 576. If your GCF is 12, what is your LCM?

Solution:

Given: GCF = 12 and also product of number = 576∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 576/12Therefore, the LCM is 48.


Example 2: For two numbers, GCF = 12 and also LCM = 48. If one number is 12, find the other number.

Solution:

Given: GCF (y, 12) = 12 and also LCM (y, 12) = 48∵ GCF × LCM = 12 × (y)⇒ y = (GCF × LCM)/12⇒ y = (12 × 48)/12⇒ y = 48Therefore, the other number is 48.


Example 3: discover the GCF the 12 and also 48, if your LCM is 48.

Solution:

∵ LCM × GCF = 12 × 48⇒ GCF(12, 48) = (12 × 48)/48 = 12Therefore, the greatest typical factor of 12 and also 48 is 12.


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FAQs top top GCF the 12 and also 48

What is the GCF the 12 and also 48?

The GCF of 12 and 48 is 12. To calculation the greatest common factor (GCF) the 12 and 48, we need to variable each number (factors of 12 = 1, 2, 3, 4, 6, 12; components of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48) and also choose the greatest aspect that specifically divides both 12 and also 48, i.e., 12.

How to discover the GCF that 12 and also 48 by prime Factorization?

To find the GCF of 12 and 48, us will find the element factorization the the provided numbers, i.e. 12 = 2 × 2 × 3; 48 = 2 × 2 × 2 × 2 × 3.⇒ due to the fact that 2, 2, 3 are typical terms in the element factorization of 12 and also 48. Hence, GCF(12, 48) = 2 × 2 × 3 = 12☛ What is a element Number?

How to uncover the GCF of 12 and 48 through Long department Method?

To uncover the GCF the 12, 48 making use of long division method, 48 is divided by 12. The equivalent divisor (12) once remainder amounts to 0 is taken together GCF.

What is the Relation between LCM and also GCF of 12, 48?

The complying with equation have the right to be offered to express the relation between LCM and GCF the 12 and 48, i.e. GCF × LCM = 12 × 48.

What room the techniques to discover GCF of 12 and 48?

There space three typically used approaches to discover the GCF that 12 and also 48.

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By Listing usual FactorsBy prime FactorizationBy long Division

If the GCF the 48 and also 12 is 12, discover its LCM.

GCF(48, 12) × LCM(48, 12) = 48 × 12Since the GCF of 48 and 12 = 12⇒ 12 × LCM(48, 12) = 576Therefore, LCM = 48☛ GCF Calculator