GCF the 12 and also 48 is the largest possible number the divides 12 and 48 precisely without any type of remainder. The factors of 12 and 48 space 1, 2, 3, 4, 6, 12 and also 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 respectively. There are 3 commonly used techniques to discover the GCF the 12 and also 48 - Euclidean algorithm, lengthy division, and also prime factorization.

You are watching: What is the greatest common factor of 12 and 48

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

Answer: GCF the 12 and also 48 is 12.

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Explanation:

The GCF of 2 non-zero integers, x(12) and y(48), is the biggest positive integer m(12) that divides both x(12) and also y(48) without any kind of remainder.


Let's look in ~ the different methods because that finding the GCF the 12 and 48.

Using Euclid's AlgorithmListing usual FactorsLong department Method

GCF the 12 and also 48 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mode 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|, where X ≠ 0)

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

GCF the 12 and 48 by Listing common Factors

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

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

GCF that 12 and also 48 by long Division

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GCF the 12 and 48 is the divisor the we obtain when the remainder i do not care 0 after ~ doing long division repeatedly.

Step 2: since the remainder = 0, the divisor (12) is the GCF the 12 and also 48.

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

☛ additionally Check:


GCF the 12 and also 48 Examples


Example 1: The product of 2 numbers is 576. If their GCF is 12, what is your LCM?

Solution:

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


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


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

Solution:

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


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FAQs top top GCF that 12 and also 48

What is the GCF of 12 and 48?

The GCF the 12 and 48 is 12. To calculation the greatest usual factor (GCF) that 12 and 48, we require to element 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 exactly divides both 12 and 48, i.e., 12.

How to uncover the GCF that 12 and also 48 by element Factorization?

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

How to find the GCF of 12 and 48 by Long division Method?

To uncover the GCF that 12, 48 utilizing long department method, 48 is separated by 12. The matching divisor (12) when remainder equals 0 is taken together GCF.

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

The adhering to equation can be offered to express the relation in between LCM and also GCF the 12 and also 48, i.e. GCF × LCM = 12 × 48.

What room the methods to find GCF that 12 and also 48?

There are three generally used methods to discover the GCF the 12 and 48.

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By Listing usual FactorsBy element FactorizationBy lengthy Division

If the GCF the 48 and 12 is 12, find its LCM.

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