GCF the 12 and 48 is the largest possible number that divides 12 and also 48 exactly without any kind of remainder. The components of 12 and 48 room 1, 2, 3, 4, 6, 12 and also 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 respectively. There room 3 typically used techniques to uncover the GCF of 12 and also 48 - Euclidean algorithm, lengthy division, and also prime factorization.

You are watching: What is the gcf of 12 and 48

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

Answer: GCF of 12 and also 48 is 12.

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Explanation:

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


Let's look in ~ the various methods for finding the GCF the 12 and also 48.

Using Euclid's AlgorithmListing typical FactorsLong division Method

GCF that 12 and 48 by Euclidean Algorithm

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

Here X = 48 and also Y = 12

GCF(48, 12) = GCF(12, 48 mode 12) = GCF(12, 0)GCF(12, 0) = 12 (∵ GCF(X, 0) = |X|, whereby X ≠ 0)

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

GCF the 12 and 48 through Listing usual Factors

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

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

GCF the 12 and 48 by long Division

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GCF of 12 and 48 is the divisor that we acquire when the remainder becomes 0 ~ doing long department repeatedly.

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

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

☛ likewise Check:


GCF of 12 and also 48 Examples


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

Solution:

Given: GCF = 12 and product of numbers = 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, discover 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 that 12 and 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 48 is 12.


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FAQs on GCF of 12 and 48

What is the GCF the 12 and also 48?

The GCF the 12 and 48 is 12. To calculate the greatest usual factor (GCF) of 12 and 48, we require to factor 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 also choose the greatest aspect that specifically divides both 12 and also 48, i.e., 12.

How to find the GCF the 12 and 48 by element Factorization?

To uncover the GCF the 12 and also 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 typical terms in the prime factorization that 12 and also 48. Hence, GCF(12, 48) = 2 × 2 × 3 = 12☛ What is a prime Number?

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

To uncover the GCF of 12, 48 utilizing long division method, 48 is separated by 12. The matching divisor (12) as soon as remainder amounts to 0 is taken as GCF.

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

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

What are the approaches to uncover GCF that 12 and also 48?

There room three commonly used techniques to discover the GCF of 12 and also 48.

See more: A Color That Starts With The Letter S That Start With ' S '

By Listing common FactorsBy element FactorizationBy lengthy Division

If the GCF the 48 and 12 is 12, uncover 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