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

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

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

Answer: GCF of 12 and 48 is 12.

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Explanation:

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


Let's look at the different methods for finding the GCF that 12 and also 48.

Using Euclid's AlgorithmListing usual FactorsLong department Method

GCF that 12 and also 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 worth of GCF of 12 and 48 is 12.

GCF that 12 and also 48 by Listing typical Factors

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

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

GCF of 12 and 48 by long Division

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

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

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

☛ also Check:


GCF of 12 and 48 Examples


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

Solution:

Given: GCF = 12 and also 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 also LCM = 48. If one number is 12, find the various other number.

Solution:

Given: GCF (y, 12) = 12 and 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: discover 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 typical factor that 12 and 48 is 12.


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FAQs ~ above GCF of 12 and also 48

What is the GCF that 12 and 48?

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

How to discover the GCF of 12 and 48 by element Factorization?

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

How to find the GCF that 12 and 48 by Long department Method?

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

What is the Relation in 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 also GCF of 12 and also 48, i.e. GCF × LCM = 12 × 48.

What space the techniques to find GCF of 12 and 48?

There are three commonly used approaches to find the GCF the 12 and also 48.

See more: How Many Cups Of Water Make A Liter, Understanding Your Measurements

By Listing typical FactorsBy prime FactorizationBy long Division

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

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