GCF that 12 and also 42 is the largest feasible number that divides 12 and also 42 precisely without any type of remainder. The factors of 12 and 42 room 1, 2, 3, 4, 6, 12 and 1, 2, 3, 6, 7, 14, 21, 42 respectively. There room 3 typically used techniques to discover the GCF that 12 and also 42 - element factorization, Euclidean algorithm, and long division.

You are watching: What is the gcf of 12 and 42

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

Answer: GCF that 12 and 42 is 6.

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Explanation:

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


Let's look at the different methods because that finding the GCF the 12 and also 42.

Listing usual FactorsPrime administer MethodUsing Euclid's Algorithm

GCF the 12 and 42 by Listing typical Factors

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

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

GCF of 12 and also 42 by element Factorization

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

GCF the 12 and 42 through Euclidean Algorithm

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

Here X = 42 and Y = 12

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

Therefore, the value of GCF that 12 and 42 is 6.

☛ likewise Check:


GCF the 12 and 42 Examples


Example 1: The product of 2 numbers is 504. If your GCF is 6, what is their LCM?

Solution:

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


Example 2: find the greatest number that divides 12 and 42 exactly.

Solution:

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

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

Therefore, the GCF the 12 and 42 is 6.


Example 3: For 2 numbers, GCF = 6 and LCM = 84. If one number is 12, discover the various other number.

Solution:

Given: GCF (y, 12) = 6 and also 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 top top GCF of 12 and 42

What is the GCF of 12 and 42?

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

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

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

How to discover the GCF that 12 and also 42 by Long department Method?

To uncover the GCF the 12, 42 using long department method, 42 is divided by 12. The equivalent divisor (6) when remainder equals 0 is taken together GCF.

What are the techniques to uncover GCF of 12 and 42?

There room three generally used techniques to find the GCF that 12 and also 42.

See more: If A Dna Sample Were Composed Of 15% Adenine, What Would Be The Percentage Of Guanine?

By long DivisionBy element FactorizationBy Listing usual Factors

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

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

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

The adhering to equation can be used to refer the relation between LCM and also GCF the 12 and also 42, i.e. GCF × LCM = 12 × 42.