GCF the 12 and 42 is the largest feasible number the divides 12 and 42 exactly without any kind of remainder. The determinants of 12 and also 42 are 1, 2, 3, 4, 6, 12 and 1, 2, 3, 6, 7, 14, 21, 42 respectively. There space 3 commonly used approaches to find the GCF the 12 and also 42 - element factorization, Euclidean algorithm, and long division.

You are watching: Greatest common factor of 12 and 42

1.GCF of 12 and also 42
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF the 12 and also 42 is 6.

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Explanation:

The GCF of two non-zero integers, x(12) and also y(42), is the biggest positive essence m(6) the divides both x(12) and y(42) without any type of remainder.


Let's look in ~ the various methods because that finding the GCF the 12 and 42.

Listing common FactorsPrime factorization MethodUsing Euclid's Algorithm

GCF of 12 and 42 by Listing typical Factors

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Factors of 12: 1, 2, 3, 4, 6, 12Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42

There room 4 common factors of 12 and also 42, that space 1, 2, 3, and also 6. Therefore, the greatest common factor that 12 and 42 is 6.

GCF that 12 and 42 by element Factorization

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Prime administrate of 12 and also 42 is (2 × 2 × 3) and also (2 × 3 × 7) respectively. As visible, 12 and also 42 have typical prime factors. Hence, the GCF that 12 and also 42 is 2 × 3 = 6.

GCF of 12 and 42 by Euclidean Algorithm

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

Here X = 42 and also Y = 12

GCF(42, 12) = GCF(12, 42 mode 12) = GCF(12, 6)GCF(12, 6) = GCF(6, 12 mode 6) = GCF(6, 0)GCF(6, 0) = 6 (∵ GCF(X, 0) = |X|, wherein X ≠ 0)

Therefore, the worth of GCF of 12 and also 42 is 6.

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GCF the 12 and also 42 Examples


Example 1: The product of two numbers is 504. If their GCF is 6, what is their LCM?

Solution:

Given: GCF = 6 and product of number = 504∵ LCM × GCF = product that numbers⇒ LCM = Product/GCF = 504/6Therefore, the LCM is 84.


Example 2: discover the biggest number the divides 12 and 42 exactly.

Solution:

The best number the divides 12 and also 42 precisely is their greatest usual factor, i.e. GCF the 12 and 42.⇒ components of 12 and also 42:

Factors of 12 = 1, 2, 3, 4, 6, 12Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42

Therefore, the GCF that 12 and 42 is 6.


Example 3: For two numbers, GCF = 6 and LCM = 84. If one number is 12, discover the various other number.

Solution:

Given: GCF (y, 12) = 6 and LCM (y, 12) = 84∵ GCF × LCM = 12 × (y)⇒ y = (GCF × LCM)/12⇒ y = (6 × 84)/12⇒ y = 42Therefore, the other number is 42.


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FAQs ~ above GCF that 12 and 42

What is the GCF that 12 and 42?

The GCF of 12 and 42 is 6. To calculate the greatest usual factor (GCF) of 12 and 42, we need to variable each number (factors that 12 = 1, 2, 3, 4, 6, 12; determinants of 42 = 1, 2, 3, 6, 7, 14, 21, 42) and also choose the greatest element that precisely divides both 12 and 42, i.e., 6.

If the GCF the 42 and also 12 is 6, find its LCM.

GCF(42, 12) × LCM(42, 12) = 42 × 12Since the GCF of 42 and also 12 = 6⇒ 6 × LCM(42, 12) = 504Therefore, LCM = 84☛ Greatest typical Factor Calculator

How to discover the GCF of 12 and also 42 through Long department Method?

To find the GCF of 12, 42 making use of long division method, 42 is divided by 12. The corresponding divisor (6) as soon as remainder amounts to 0 is taken as GCF.

What are the methods to find GCF of 12 and also 42?

There space three typically used methods to find the GCF that 12 and also 42.

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By lengthy DivisionBy prime FactorizationBy Listing usual Factors

How to uncover the GCF the 12 and 42 by element Factorization?

To uncover the GCF that 12 and 42, us will find the prime factorization the the given numbers, i.e. 12 = 2 × 2 × 3; 42 = 2 × 3 × 7.⇒ since 2, 3 are common terms in the element factorization of 12 and also 42. Hence, GCF(12, 42) = 2 × 3 = 6☛ element Number

What is the Relation between LCM and GCF the 12, 42?

The complying with equation have the right to be provided to express the relation in between LCM and also GCF the 12 and 42, i.e. GCF × LCM = 12 × 42.